Teacher Page. Algebra/ Day #3 90 Minute Class Proportions, Percents, Percent Change, Scientific Notation

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1 Teacher Page Algebra/ Day #3 90 Minute Class Proportions, Percents, Percent Change, Scientific Notation 9-12.A.1.19 Use the four basic operations (+, -,, ) in contextual situations with numbers in scientific notation, and express the results with the appropriate number of significant figures. Multiple Choice: 1 Point 1. If the speed of light is 3.00 x 10 8 meters per second, how far would a beam of light travel in 7500 seconds? A x 10 8 m D x m B x 10 8 m E x m C x m 2. 4 x = 12 9 A. 3 D. 27 B. 5.3 E C A lumberjack (person who cuts down trees) wants to know the height of a tree. The lumberjack measures the shadow of his friend, who is 5 feet tall and standing beside the tree, and measures the shadow of the tree. If his friend s shadow is 12 feet long and the tree s shadow is 60 feet long, how tall is the tree? 3.

2 4. Tax on a $25 item is $2.06. A. What should the tax be on a $45 item? B. If the tax is $4.32, what is the cost of the item? C. If the $25 item and $45 item and the cost of the third item, with the tax of $4.32, was totaled and the tax was included what would be the total bill become? 4.

3 Teacher Page Answer Key Algebra/ Day #3 90 Minute Class Proportions, Percents, Percent Change, Scientific Notation Multiple Choice: 1 Point 1. If the speed of light is 3.00 x 10 8 meters per second, how far would a beam of light travel in 7500 seconds? A x 10 8 m D x m B x 10 8 m E x m C x m D Multiply 3.00 x 10 8 times Make sure your answer is in scientific notation x = 12 9 A. 3 D. 27 B. 5.3 E C. 4 A To solve, cross-multiply then divide. : 2 Points 3. A lumberjack (person who cuts down trees) wants to know the height of a tree. The lumberjack measures the shadow of his friend, who is 5 feet tall and standing beside the tree, and measures the shadow of the tree. If his friend s shadow is 12 feet long and the tree s shadow is 60 feet long, how tall is the tree? 25 ft. x 60 = 5 12 (2 points) 12x = 300 x = 25

4 : 4 Points 4. Tax on a $25 item is $2.06. B. What should the tax be on a $45 item? C. If the tax is $4.32, what is the cost of the item? D. If the $25 item and $45 item and the cost of the third item, with the tax of $4.32, was totaled and the tax was included what would be the total bill become? A. $3.71 (1 point) B. $52.43 (1 point) C. $ (2 points) First, find the tax rate. Divide 2.06 by 25 for a tax rate of 8.24%. A.) Multiply $45 times 8.24%, which equals $3.71 B.) Divide $4.32 by 8.24%, which equals $54.43 C.) Add ( ) + ( ) + ( ) = $132.52

5 Name: Date: Per: Student Page: Algebra/ Day # 3 Proportions, Percents, Percent Change, Scientific Notation 1. A survey poll was taken one week before an election. Candidate Percent of Supporters Beaver 35% Lemur x Other 20% Write the percentage of those who support Candidate Lemur as a fraction in simplest form. A B. 1 5 C D E If the speed of light is 3.00 x 10 8 meters per second, how far would a beam of light travel in 7500 seconds? A x 10 8 m D x m B x 10 8 m E x m C x m

6 4. 3 x = A. 2 D. 0.5 B E. no solution C The tax rate in Portville is 6.75% with Felicia buying $215 worth of groceries. A. How much is the tax on her groceries? B. What is the total bill? C. Next week Felicia paid a total of $ for groceries, what was the amount of taxes she paid for both weeks? 5.

7 6. In 2000, the population of Thomasville, North Carolina, was about 20,000 people. Write this population in scientific notation. A. 0.2 x 10 5 m D. 20 x 10 3 m B. 2 x 10 4 m E. 25 x10 4 m C. 2 x 10 5 m 7. A U. S. one dollar coin is made of Copper, Zinc, Manganese, and Nickel in the following ratio 44 : 3 :2 : 1. Its mass is eight grams. A. How many grams of each element are used in a one dollar coin? B. If the ratio was changed to 32 : 6 : 4 : 8, how much Copper is used? Olga plans to take a trip from her house in San Marcos, Texas to a friends house in Zapata, Texas. She measured the distance between the two places on a map and found it to be 8 inches. A. If the scale on the map is ½ inch represents 14 miles, what is the actual distance between the two towns? B. If it is 566 mile to Roswell from San Marcos, how many inches are between the two places on the map if it is a straight line? 8.

8 9. New Mexico s population in 1990 was about 1,500,000. The population in 2000, was about 1,800,000. A. What is the percent increase during this 10 year period? B. If this increase were to continue, what would be the approximate population for New Mexico in the year 2010? A.) Find the percent change from 24 to 72. B.) Is this a percent increase or decrease? 10.

9 Student Page Answer Key Algebra/ Day # 3 Proportions, Percents, Percent Change, Scientific Notation 1. A survey poll was taken one week before an election. Candidate Percent of Supporters Beaver 35% Lemur x Other 20% Write the percentage of those who support Candidate Lemur as a fraction in simplest form. A. B. C. D. E. C Add the two known percentages then subtract from % as a fraction is. 2. If the speed of light is 3.00 x 10 8 meters per second, how far would a beam of light travel in 7500 seconds? A x 10 8 m D x m B x 10 8 m E x m C x m D Multiply 3.00 x 10 8 times Make sure your answer is in scientific notation.

10 4. _3x_ = _9_ 4 6 A. 2 D. 0.5 B E. no solution C. 4.5 A To solve, cross-multiply then divide. : 4 Points

11 5. The tax rate in Portville is 6.75% with Felicia buying $215 worth of groceries. A. How much is the tax on her groceries? B. What is the total bill? C. Next week Felicia paid a total of $ for groceries, what was the amount of taxes she paid for both weeks A. $14.51 (1 point) B. $ (1 point) C. $30.61 (2 points) A.) Multiply $215 times 6.75%, which equals $14.51 B.) Add: $ $14.51 = $ OR- $215 + $215(6.75%) = $ C.) x + x(6.75%) = $ x x = x = Divide both sides by x = $ Subtract $ from $ to find amount of tax, which equals $16.10 Add the two tax amounts together $ $16.10 = $ In 2000, the population of Thomasville, North Carolina, was about 20,000 people. Write this population in scientific notation. A. 0.2 x 10 5 m D. 20 x 10 3 m B. 2 x 10 4 m E. 25 x10 4 m C. 2 x 10 5 m B Move decimal four places to the left. Make sure the answer is between 1 and 10. : 2 Points

12 7. A U. S. one dollar coin is made of Copper, Zinc, Manganese, and Nickel in the following ratio 44 : 3 :2 : 1. Its mass is eight grams. A. How many grams of each element are used in a one dollar coin? B. If the ratio was changed to 32 : 6 : 4 : 8, how much Copper is used? A.) 7.04 grams of Copper; 0.48 grams of Zinc; 0.32 grams of Manganese; 0.16 grams of Nickel (1 point) B.) 5.12 grams of Copper (1 point) A.) 44 x Copper: = 50 x = 352 x = 7.04 grams 50 8 Zinc: 3 x = 50 x = 24 x = 0.48 grams 50 8 Manganese: 2 x = 50 = x x = 0.32 grams Nickel: 1 x = 50 x = 8 x = 0.16 grams 50 8 B.) Copper: 32 x 50 8 = 50 x = 256 x = 5.12 grams : 4 Points 8. Olga plans to take a trip from her house in San Marcos, Texas to a friends house in Zapata, Texas. She measured the distance between the two places on a map and found it to be 8 inches. A. If the scale on the map is ½ inch represents 14 miles, what is the actual distance between the two towns? B. If it is 566 mile to Roswell from San Marcos, how many inches are between the two places on the map if it is a straight line? A.) 224 miles B.) 20.2 inches (2 points) (2 points) A.) 0.5in. 8in. = 0.5x = mi x x = 224miles B.) 0.5 in. x = 14 x = mi. 566mi. x = 20. 2inches

13 : 4 Points 9. New Mexico s population in 1990 was about 1,500,000. The population in 2000, was about 1,800,000. A. What is the percent increase during this 10 year period? B. If this increase were to continue, what would be the approximate population for New Mexico in the year 2010? A.) 20% (2 points) B.) 2,160,000 (2 points) Formula: A.) To solve, subtract 1,500,000 from 1,800,000 to find change. Next, cross-multiply then divide to find value of x. x 300, = 1, 500,000x = 30,000, 000 x = 20% 1,500,000 B.) 1, 800, ,800,000(20%) = 2,160, 000 : 2 Points 10. A.) Find the percent change from 24 to 72. B.) Is this a percent increase or decrease? A.)200 (1 point) B.) Increase (1 point) Formula: To solve, subtract 24 from 72 to find change. Next, cross-multiply then divide to find value of x.