Section 3.2 Objectives

Transcription

1 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions Section Objectives Determine if a proportion is true or false Solve proportions for an unknown Solve unit conversion problems using proportions Solve application word problems involving proportions Page 9

2 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions SECTION Proportions INTRODUCTION In this section you will study a special type of equation called a proportion Learning about proportions is important because they have numerous real-life applications You will examine some applications yourself as you learn to set up proportions that model real-world scenarios You will also learn a special technique for solving proportions But first, let s begin with the basics what is a proportion? Think of taking two fractions and inserting an equal sign between them That s a proportion! PROPORTION Definition Math Statement Example A proportion is a statement that two ratios (fractions) are equal a c b d Read a is to b as c is to d Means Ex (Middle Terms) Extremes (Outer Terms) 6 Read is to 6 as is to Means: 6 and Extremes: and PROPORTIONS TRUE OR FALSE Proportions are either true or false We show an example of each below True If we reduce 8 8 we get The two fractions are equal False If we reduce we do not get 9 The fractions are not equal Sometimes it is difficult to determine whether a proportion is true or false by reducing and comparing the fractions For instance, it would be difficult with the proportion For that reason, there is another method that can be used to determine if a proportion is true or false The method is shown in the following box Page 9

3 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions PROPERTY OF PROPORTIONS A proportion is true if and only if the product of the extremes equals the product of the means a b c is true only if a d b c d This can be stated more simply in the following way: A proportion is true only if its cross products are equal a b = c d is true only if ad bc EXAMPLES: Determine if the proportion is true Is a true statement? = 8 Multiply diagonally to get the cross products? Perform the multiplications on each side Yes, since the cross products are equal, the proportion is true Is 0 9 a true statement? 7 09 = 7? 70 9 Multiply diagonally to get the cross products Perform the multiplications on each side 6 6 No, since the cross products are not equal, the proportion is not true PRACTICE: Determine if the proportion is true Is 7 8 a true statement? Is 8 a true statement? 6 7 Answers: No Yes Page 96

4 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions SOLVING A PROPORTION A proportion contains four numbers But in some proportions, only three of the numbers are given and a variable represents the fourth In these types of problems, our goal will be to determine the value of the variable that makes the proportion true We will solve for the variable using a technique involving the cross products The complete procedure is explained below SOLVING A PROPORTION To solve a proportion for a variable: Set the cross products equal to each other by cross multiplying Perform the multiplication on both sides of the equation To isolate the variable, divide both sides of the equation by the coefficient EXAMPLES: Solve each proportion Solve for n: 7 00 This equation is a proportion n 7 00 n 7 n 00 7n 00 7n n 00 Set the cross products equal to each other by cross multiplying Perform the multiplication on both sides of the equation To isolate the variable, divide by 7 on both sides of the equation This is the answer Solve for x: x 7 x 7 x x x x This equation is a proportion 7 Set the cross products equal to each other by cross multiplying Perform the multiplication on both sides of the equation To isolate the variable, divide by on both sides of the equation This is the answer Page 97

5 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions Solve for n: This equation is a proportion n n n n n n n OR n This is the answer Set the cross products equal to each other by cross multiplying Perform the multiplication on both sides of the equation To isolate the variable, divide by on both sides of the equation Solve for n: n This equation is a proportion Begin by changing the mixed number to an improper fraction n n 0 n n n 0 n n n Set the cross products equal to each other by cross multiplying Perform the multiplication on both sides of the equation To isolate the variable, divide by on both sides of the equation Rewrite the left side of the equation as a division of two fractions Multiply the first fraction by the reciprocal of the second fraction Divide out common factors n OR n This is the answer Page 98

6 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions PRACTICE: Solve each proportion Solve for n: 9 n Solve for n: n Solve for x: x 6 0 Solve for n: 6 n Solve for x: 7 x 9 6 Solve for n: n 8 Answers: n n x 9 n x 6 7 n 6 APPLICATIONS OF PROPORTIONS You are in the grocery store because you need to purchase eggs You are going to make cupcakes for a family reunion Your recipe makes 8 cupcakes and requires eggs But you want to make dozen cupcakes this is going to be a large reunion How many eggs will you need to buy? Looks like you have a proportion problem that needs to be solved! In this type of application, we are dealing with quantities that are proportional The number of cupcakes you bake is proportional to the number of eggs you use To make 8 cupcakes you need eggs If you wanted to double the number of cupcakes and make 6, then you would have to double the number of eggs and use 6 If you wanted to triple the number of cupcakes and make, then you would have to triple the number of eggs and use 9 But you have decided to make dozen cupcakes which is 8 cupcakes The number of eggs is not so easy to calculate for 8 cupcakes So, we will use algebra We will set up a proportion to solve the problem Study the steps of the procedure and the solution that follows Page 99

7 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions USING PROPORTIONS TO SOLVE APPLICATION PROBLEMS Variable: Assign a variable to the unknown quantity Ratio in Words: Set up a fraction using words to identify the two quantities being compared Known Ratio: Write a fraction using the two given values that relate the two quantities Make sure the fraction is set up like Step Unknown Ratio: Write another fraction involving the variable Make sure the fraction is set up like Step Proportion: Write a proportion by setting the ratios (fractions) equal to each other 6 Solve: Solve the proportion using cross products and inverse operations EXAMPLES: Solve each problem by using a proportion A recipe that makes 8 cupcakes requires eggs How many eggs are needed to make dozen, or 8, cupcakes? STEP : Variable assign variable to unknown quantity STEP : Ratio in Words fraction with quantities being compared STEP : Known Ratio fraction with given values, set up like step STEP : Unknown Ratio fraction involving the variable, set up like step n = number of eggs to make dozen cupcakes # of Cupcakes # of Eggs 8 Cupcakes Eggs 8 Cupcakes n Eggs NOTE: In all three ratios above, cupcakes were in the numerator of the fraction and eggs in the denominator It is very important to be consistent when you set up your fractions STEP : Proportion set ratios equal 8 8 n STEP 6: Solve set cross products equal 8n divide to isolate the variable 8n 8 8 Answer: You will need 8 eggs to bake 8 cupcakes n 8 Page 00

8 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions Water is being pumped out of a basement at a rate of 0 gallons per hour How many hours will it take to pump 00 gallons of water out of the basement? STEP : Variable assign variable to unknown quantity STEP : Ratio in Words fraction with quantities being compared STEP : Known Ratio fraction with given values, set up like step STEP : Unknown Ratio fraction involving the variable, set up like step n = number of hours to pump 00 gal of water out gallons of Water Number of hours 0 gallons hour 00 gallons n hours NOTE: In all three ratios above, gallons were in the numerator of the fraction and hours in the denominator It is very important to be consistent when you set up your fractions STEP : Proportion set ratios equal 0 00 n STEP 6: Solve set cross products equal and isolate the variable 0n 00 0n Answer: It will take hours to pump 00 gallons of water out n You need to combine 98 grams of sulfuric acid and 70 grams of sodium hydroxide to produce sodium sulfate (a kind of chemical salt) How many grams of sulfuric acid would need to combine with 0 grams of sodium hydroxide to produce sodium sulfate? STEP : Variable assign variable to unknown quantity n = grams of sulfuric acid to combine with 0 grams of sodium hydroxide STEP : Ratio in Words fraction with quantities being compared STEP : Known Ratio fraction with given values grams of Sulfuric Acid grams of Sodium Hydroxide 98 grams of SA 70 grams of SH STEP : Unknown Ratio fraction involving the variable n grams of SA 0 grams of SH NOTE: In all three ratios above, Sulfuric Acid was in the numerator and Sodium Hydroxide was in the denominator It is very important to be consistent when you set up your fractions STEP : Proportion set ratios equal 98 n 70 0 STEP 6: Solve set cross products equal and isolate the variable n Answer: You need 8 grams of Sulfuric Acid to combine with 0 grams of Sodium Hydroxide n n Page 0

9 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions You know that there are 6 milligrams of cholesterol in ounces of trout How much cholesterol is there in 8 ounces of trout? STEP : Variable assign variable to unknown STEP : Ratio in Words quantities being compared n = mg of cholesterol in 8 oz of trout mg of Cholesterol ounces of Trout STEP : Known Ratio fraction with given values 6 mg of Cholesterol ounces of Trout STEP : Unknown Ratio fraction involving variable n mg of Cholesterol 8 ounces of Trout NOTE: In all three ratios, Cholesterol was in the numerator and Trout in the denominator 6 n STEP : Proportion set ratios equal 8 rewrite the mixed number as 6 n an improper fraction 7 8 STEP 6: Solve set cross products equal 8 7 n multiply both sides of the equation by the LCD 7 8 n 8 7 n 896 7n Answer: There are 8 mg of cholesterol in 8 ounces of trout 896 7n n PRACTICE: Solve each problem by using a proportion To make a cup of hot cocoa, Bob mixes teaspoons of cocoa powder with cups of milk How much cocoa powder would be needed to mix with cups of milk? Water is pumped into a pool at a rate of 0 gallons per hour How many hours will it take to pump 000 gallons of water into the pool? You need to combine 98 grams of sulfuric acid (HSO) and 80 grams of sodium hydroxide (NaOH) to produce sodium sulfate (a kind of chemical salt) How many grams of sulfuric acid (HSO) would you need to combine with 0 grams of sodium hydroxide (NaOH) to produce sodium sulfate? A single tablet of One-A-Day Vitamin for men contains 7 milligrams of Vitamin C How many milligrams of Vitamin C are in tablets of One-A-Day Vitamins? Answers: 8 teaspoons 9 grams hours 7 milligrams Page 0

10 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions CONVERSIONS USING PROPORTIONS Measurement is very important to everyday life We measure distance, time, weight, space, and many other aspects of our physical world From one culture to another culture, or even within the same community, a particular aspect may be measured in different ways using different units of measurement For example, the length of a full semester credit course at CCBC could be given as 7 hours or as 0 minutes An important skill is learning to convert from one type of measuring unit to another Unit conversion problems can be solved with proportions using the same procedure that we used to solve application problems The steps are reviewed below USING PROPORTIONS TO PERFORM UNIT CONVERSIONS Variable: Assign a variable to the unknown quantity Ratio in Words: Set up a fraction using words to identify the two units being compared Known Ratio: Write a fraction using the given conversion fact that relates the two units Unknown Ratio: Write another fraction involving the variable Proportion: Write a proportion by setting the ratios (fractions) equal to each other 6 Solve: Solve the proportion using cross products and inverse operations There are two primary systems of measurement that we will study, the US System of Measurement and the Metric System of Measurement We begin with the US System CONVERSIONS WITHIN THE US SYSTEM You are probably most familiar with the system of measurement that we use here in the United States The units of measurement are typically categorized based on what they measure: length, time, volume, and weight The chart below lists the basic unit conversion facts in each category BASIC CONVERSION FACTS US SYSTEM OF MEASUREMENT LENGTH inches (in) = foot (ft) feet (ft) = yard (y) 80 feet (ft) = mile (mi) WEIGHT 6 ounces (oz) = pound (lb) 000 pounds (lbs) = ton (T) VOLUME 8 fluid ounces (fl oz) = cup (c) cups (c) = pint (pt) pints (pt) = quart (qt) quarts (qt) = gallon (gal) TIME 60 seconds (s) = minute (min) 60 minutes (min) = hour (hr) hours (hrs) = day 7 days = week 6 days = year Page 0

11 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions Now we will convert a measurement from one unit to another by setting up and solving a proportion The given conversion fact will be used as the known ratio in the proportion EXAMPLES: Perform each unit conversion by using a proportion Convert feet to inches Use the conversion fact: inches (in) = foot (ft) STEP : Variable assign variable to unknown STEP : Ratio in Words fraction using units being compared STEP : Known Ratio fraction using given conversion fact STEP : Unknown Ratio fraction using variable n = inches equal to feet inches feet in foot NOTE: In all three ratios above, inches were in the numerator and feet in the denominator It is very important to be consistent when you set up your fractions STEP : Proportion set ratios equal n STEP 6: Solve set cross products equal 60 n n in ft Answer: feet is equal to 60 inches n 60 Convert 0 inches to feet Use the conversion fact: inches (in) = foot (ft) STEP : Variable assign variable to unknown STEP : Ratio in Words fraction using units being compared STEP : Known Ratio fraction using given conversion fact STEP : Unknown Ratio fraction using variable NOTE: n = feet equal to 0 inches inches feet in foot 0 in n ft In all three ratios above, inches were in the numerator and feet in the denominator It is very important to be consistent when you set up your fractions STEP : Proportion set ratios equal 0 n STEP 6: Solve set cross products equal n 0 isolate the variable simplify Answer: 0 inches is equal to feet n 0 0 n n Page 0

12 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions Convert pounds to ounces Use the conversion fact: 6 ounces (oz) = pound (lb) STEP : Variable assign variable to unknown n = ounces equal to pounds STEP : Ratio in Words fraction using units being compared STEP : Known Ratio fraction using given conversion fact STEP : Unknown Ratio fraction using variable NOTE: In all ratios, ounces are in the numerator, pounds in the denominator STEP : Proportion set ratios equal STEP 6: Solve set cross products equal Answer: write the mixed number as an improper fraction divide out common factors pounds is equal to 60 ounces ounces pounds 6 ounces pound n ounces pounds 6 n n n n 60 n The solutions for the next three examples are presented using a shortened format Convert hours to minutes Use the conversion fact: 60 minutes (min) = hour (hr) VARIABLE UNITS PROPORTION ANSWER n = minutes equal to hours min hr 60 n 0 n hours is equal to 0 minutes Convert 0 fluid ounces to cups Use the conversion fact: 8 fluid ounces (fl oz) = cup (c) VARIABLE UNITS PROPORTION ANSWER n = cups equal to 0 fl oz fl oz cups 8 0 n 8n 0 8n n 0 fl oz is equal to cups 6 Convert 0 quarts to gallons Use the conversion fact: quarts (qt) = gallon (gal) VARIABLE UNITS PROPORTION ANSWER n = gallons equal to 0 quarts qt gal 0 n n 0 n 0 n 7 0 quarts is equal to 7 gallons Page 0

13 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions PRACTICE: Perform each unit conversion by using a proportion Convert miles to feet Use the conversion fact: 80 feet (ft) = mile (mi) Convert 8 feet to yards Use the conversion fact: feet (ft) = yard (y) Convert minutes to seconds Use the conversion fact: 60 seconds (s) = minute (min) Convert 96 hours to days Use the conversion fact: hours (hrs) = day Convert 8 pints to cups Use the conversion fact: cups (c) = pint (pt) 6 Convert pints to quarts Use the conversion fact: pints (pt) = quart (qt) 7 Convert 600 pounds to tons Use the conversion fact: 000 pounds (lbs) = ton (T) 8 Convert pounds to ounces Use the conversion fact: 6 ounces (oz) = pound (lb) Answers:,0 ft 7 yds 00 sec days 7 c 6 qt 7 T 8 0 oz CONVERSIONS WITHIN THE METRIC SYSTEM The metric system is an international system of measurement based on powers of ten The system has three basic units that correspond to what is being measured: length, volume, or weight Prefixes can be attached to the basic units to form smaller or larger units of measure BASIC UNITS The metric system of measurement uses the following basic units for length, volume, and weight Meter: The basic unit of length is the meter The abbreviation for meter is m A meter is about inches longer than a yard Michael Jordan is about meters tall Liter: The basic unit of volume is the liter The abbreviation for liter is L A liter is slightly less than a quart It takes about 0 liters of gasoline to fill a Mini Cooper s gas tank Gram: The basic unit of weight is the gram The abbreviation for gram is g About 0 grams equal an ounce The average weight of a healthy newborn baby is about,000 grams PREFIXES In the metric system, a prefix can be attached to any of the basic units to produce a new unit The new unit is smaller or larger than the basic unit by a power of 0 The table below shows some of the common prefixes and their meanings The table shows, for example, that a kilogram (kg) is larger than a gram because one kilogram is equal to one thousand grams The table also shows, for example, that a centimeter (cm) is smaller than a meter because one centimeter is equal to one hundredth of a meter Prefix KILO k- HECTO h- DEKA da- BASIC UNIT DECI d- CENTI c- MILLI m- Meaning Thousand Hundred Ten (m, L, g) Tenth Hundredth Thousandth, Page 06

14 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions Now we will express the information in the prefix table using conversion facts as we did for the US System of Measurement The conversion facts are shown using meters However, meter (the basic unit for length) could be replaced with liter (the basic unit for volume) or with gram (the basic unit for weight) BASIC CONVERSION FACTS METRIC SYSTEM OF MEASUREMENT BASIC UNITS Meter (m) to measure length Liter (L) to measure volume Gram (g) to measure weight PREFIXES (shown for meter) kilometer (km) = 000 meters (m) hectometer (hm) = 00 meters (m) dekameter (dam) = 0 meters (m) 0 decimeters (dm) = meters (m) 00 centimeters (cm) = meter (m) 000 millimeters (mm) = meter (m) Now we will convert a measurement from one unit to another by setting up and solving a proportion The given conversion fact will be used as the known ratio in the proportion EXAMPLES: Perform each unit conversion by using a proportion Convert kilometers (km) to meters (m) Use the conversion fact: kilometer (km) = 000 meters (m) STEP : Variable assign variable to unknown STEP : Ratio in Words fraction using units being compared STEP : Known Ratio fraction using given conversion fact STEP : Unknown Ratio fraction using variable NOTE: n = meters equal to kilometers km m km 000 m km n m In all three ratios, kilometers were in the numerator and meters in the denominator It is very important to be consistent when you set up your fractions STEP : Proportion set ratios equal STEP 6: Solve set cross products equal 000 n Answer: kilometers equals 000 meters n 000 Page 07

15 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions Convert 88 centigrams (cg) to grams (g) Use the conversion fact: 00 centigrams (cg) = gram (g) VARIABLE UNITS PROPORTION ANSWER n = grams equal to 88 centigrams cg g n 00n 88 00n n centigrams equals 088 grams Convert liters (L) to kiloliters (kl) Use the conversion fact: kiloliter (kl) = 000 liters (L) VARIABLE UNITS PROPORTION ANSWER n = kiloliters equal to liters kl L n n 000n n liters equals 00 kiloliters PRACTICE: Perform each unit conversion by using a proportion Convert kilograms (kg) to grams (g) Use the conversion fact: kilogram (kg) = 000 grams (g) Convert 6 centimeters (cm) to meters (m) Use the conversion fact: 00 centimeters (cm) = meter (m) Convert 9 meters (m) to millimeters (mm) Use the conversion fact: 000 millimeters (mm) = meter (m) Convert 0 kiloliters (kl)to liters (L) Use the conversion fact: kiloliter (kl) = 000 liters (L) Convert 8 liters (L) to milliliters (ml) Use the conversion fact: 000 milliliters (ml) = liter (L) 6 Convert 970 milligrams (mg) to grams (g) Use the conversion fact: 000 milligrams (mg) = gram (g) Answers: 0 g 006 m 900 mm 00 L 80 ml 6 97 g Page 08

16 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions SECTION SUMMARY Proportions PROPORTION TRUE OR FALSE PROPORTION A statement that two ratios (fractions) are equal a c only if ad bc b d Multiply diagonally to get the cross products If the cross products are equal, the proportion is true Example: 8 Example: Is 6 a true statement? 8 9? ( 6)(9 ) (8)() No, the proportion is not true SOLVING A PROPORTION Multiply diagonally and set the cross products equal to each other Isolate the variable using inverse operations Example: 6 n n 6 n 90 n 90 n APPLICATION PROBLEMS Assign Variable to Unknown Write Ratio in Words Write Proportion: Ratio of Given Values = Ratio with Variable Solve Proportion Example: On a map, cm represents 9 km How many cm would represent 6 km? n = centimeters equal to 6 km Centimeters Kilometers n n 7 9n 7 9n n So, 6 km would be represented by 8 cm UNIT CONVERSIONS Assign Variable to Unknown Write Ratio in Words Write Proportion: Ratio of Conversion Fact = Ratio with Variable Solve Proportion Example: Convert minutes to seconds Use the fact: 60 seconds (s) = minute (min) n = seconds equal to minutes Minutes Seconds 60 n n 60 n 80 So, minutes equals 80 seconds Page 09

17 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions SECTION EXERCISES Proportions Determine if the following proportions are true Solve the proportions For problems involving decimals, give the answer in decimal form For problems involving fractions, give the answer in fractional form 6 7 n 7 0 n 0 0 n n n n 9 8 n 7 n 6 Solve each problem by using a proportion Harry gets miles per gallon of gasoline in his truck How many miles can Harry drive on gallons of gasoline? On a map, centimeters represents kilometers How many kilometers are represented by centimeters? A nurse has to give a patient a dose of medication The dosage says to administer ml of medication for a 0 pound person If the patient weighs 00 pounds, how many ml of medication should the nurse give to the patient? To make moles of water, moles of oxygen gas are needed How many moles of oxygen gas are needed to make moles of water? Three ounces of a chemical are needed to treat ounces of water How many ounces of water can be treated with ounces of the chemical? Page 0

18 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions 6 A nurse has to give a child a dose of Tylenol The dosage says to administer teaspoons of medication for a 0 pound person If the child weighs 7 pounds, how many teaspoons of medication should the nurse give to the child? 7 A college has a ratio of male students for every female students If there are male students, how many female students attend the college? 8 An office assistant can type words in minutes At this rate, how many minutes would it take the office assistant to type 00 words? 9 There are mg of cholesterol in ounces of egg substitute How many mg of cholesterol are there in ounces of egg substitute? 0 A recipe calls for ¼ teaspoon of salt for every ½ cup of flour How much salt should be used for cups of flour? Perform each unit conversion by using a proportion Convert 8 inches to feet Use the conversion fact: inches (in) = foot (ft) Convert 8,80 feet to miles Use the conversion fact: 80 feet (ft) = mile (mi) Convert 6 yards to feet Use the conversion fact: feet (ft) = yard (y) Convert 600 seconds to minutes Use the conversion fact: 60 seconds (s) = minute (min) Convert hours to minutes Use the conversion fact: 60 minutes (min) = hour (hr) 6 Convert cups to fluid ounces Use the conversion fact: 8 fluid ounces (fl oz) = cup (c) 7 Convert 7 quarts to pints Use the conversion fact: pints (pt) = quart (qt) 8 Convert 6 gallons to quarts Use the conversion fact: quarts (qt) = gallon (gal) 9 Convert tons to pounds Use the conversion fact: 000 pounds (lbs) = ton (T) 0 Convert 0 ounces to pounds Use the conversion fact: 6 ounces (oz) = pound (lb) Perform each unit conversion by using a proportion Convert 68 kilometers to meters Use the conversion fact: kilometer (km) = 000 meters (m) Convert 87 meters to centimeters Use the conversion fact: 00 centimeters (cm) = meter (m) Convert 600 millimeters to meters Use the conversion fact: 000 millimeters (mm) = meter (m) Convert 800 milliliters to liters Use the conversion fact: 000 milliliters (ml) = liter (L) Convert 90 grams to kilograms Use the conversion fact: kilogram (kg) = 000 grams (g) 6 Convert 0 grams to milligrams Use the conversion fact: 000 milligrams (mg) = gram (g) Page

19 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions Answers to Section Exercises True False n n 6 n 0 OR n 6 n 9 7 n 8 n 0 9 n 0 n 6 OR n miles kilometers ml moles of oxygen gas 00 ounces of water 6 teaspoons females 8 0 minutes 9 67 mg 0 teaspoons 7 ft mi 8 ft 0 min min 6 0 fl oz 7 pts 8 6 qts lbs 0 lbs 6800 m 87 cm 6 m 08 L 09 kg 6 0mg Page

20 CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions Mixed Review Sections Evaluate b a c if a, Simplify x 8y 6 7x y 0 Simplify x Solve a a 7 b, and c Translate the word problem into an algebraic equation Then solve the equation The difference of a number and is five times the number Determine the number 6 Write an algebraic equation for the word problem Then solve the equation to answer the question Austin wants to buy a guitar that costs $780 He has already saved $0 If he can save $0 per month, how long will it take him to save enough to buy the guitar? 7 Solve x x 8 Solve x 6 8, graph the solution, and write the solution in interval notation 9 The formula used to determine the perimeter of a rectangle is P L W where L is the length and W is the width Find L if P and W 0 In the equation x6y 0, solve for x Answers to Mixed Review x6y 6x 0 a nn n 6 0x months 7 x 8 x [, ) 9 L 6 0 x 9y [ Page