Chapter 1 Math in the Real World Solve each problem. Copy important information and show all work in your spiral notebook. 1. A rectangular shape has a length-to-width ratio of approximately 5 to 3. A designer 1 can use the expression (5w) to find the length of such a rectangle with given width w. 3 Find the length of such a rectangle with width 6 inches. 2. A bank charges interest on money it loans. Interest is sometimes a fixed amount of the loan. The expression a ( 1 + i ) gives the total amount due for a loan of a dollars with interest rate i, where i is written as a decimal. Find the total amount due for a loan of $100 with an interest rate of 10% (Hint: 10% = 0.1) 3. There are 24 frames, or still shots, in one second of movie footage. To determine the number of frames in a movie, you can use the expression (24)(60)m, where m is the running times in minutes. E.T. the Extra-Terrestrial has a running time of 115 minutes. Determine how many frames are in the movie. 4. A basketball league has 288 players and 24 teams, with an equal number of players per team. If the number of teams is reduced by 6 but the total number of players stays the same, there will be players per team. (A) 6 more (B) 4 more (C) 4 fewer (D) 6 fewer 5. Mark is going to work for his father s pool cleaning business during the summer. Mark s father will pay him $5 for each pool he helps clean. Write an algebraic expression to determine how much Mark will earn if he cleans n pools. Then evaluate the expression for 15, 25, 35, and 45 pools. 6. Write a word problem (tell me a story!) that can be evaluated by the algebraic expression x 450. Then evaluate the expression for x = 1325. 7. A community center is trying to raise $1680 to purchase exercise equipment. The center is hoping to receive equal contributions from members of the community. Write an algebraic expression to determine how much will be needed from each person if n people contribute. Then evaluate the expression for 10, 12, 14, and 16 people.
8. Write a word problem that can be evaluated by the algebraic expression 372 + r. Then evaluate the expression for r = 137. 9. At the age of 2, a cat or a dog is considered 24 human years old. Each year after age 2 is equivalent to 4 human years. Let a represent the age of the cat or dog. Fill in the expression [24 + (a 2)] so that it represents the age of the cat or dog in human years. Copy the chart and use your expression to complete it. Age [24 + (a 2)] Age (human years) 2 3 4 5 6 10. A student wrote an algebraic expression for 5 less than the quotient of n and 3 as n 5. What error did the student make? Explain. 3 11. Paul used addition to solve a word problem about the weekly cost of commuting by toll road for $1.50 each day. Fran solved the same problem by multiplying. They both got the correct answer. How is this possible? 12. Write an expression for the sum of 1 and twice a number n. If you let n be any number, will the result always be an odd number? Explain. 13. After the first round of the 2005 Masters gold tournament, scores relative to par were Tiger Woods 2, Vijay Singh -4, Phil Mickelson -2, and Justin Leonard 5. Use <, >, or = to compare Vijay Singh s and Phil Mickelson s scores. Then list the golfers in order from the lowest to the highest. 14. During a very cold week, the temperature in Philadelphia was -7ºF on Monday, 4ºF on Tuesday, 2ºF on Wednesday, and -3ºF on Thursday. Use <, >, or = to compare the temperatures on Wednesday and Thursday. Then list the days in order of the coldest to the warmest.
15. The table shows the lowest recorded temperatures for each continent. Write the continents in order from the lowest recorded temperature to the highest recorded temperature. Continent Africa Antarctica Asia Australia Europe North America South America Temperature -11ºF -129ºF -90ºF -9ºF -67ºF -81ºF -27ºF 16. The boiling point of nitrogen is -196ºC. The boiling point of oxygen is -183ºC. Which element has the higher boiling point? Explain. 17. Explain why there is no number that can replace n to make the equation n = -1 true. 18. Lee opens a checking account. In the first month, he makes two deposits and writes three checks, as shown in the table. Find what his balance is at the end of the month. (Hint: Checks count as negative amounts) Checks Deposits $134 $600 $56 $225 $302 19. On Monday morning, a mechanic has no cars in her shop. The table shows the number of cars dropped off and picked up each day. Find the total number of cars left in her shop on Friday. Cars Dropped Off Cars Picked Up Monday 8 4 Tuesday 11 6 Wednesday 9 12 Thursday 14 9 Friday 7 6 20. A student evaluated -4 + d for d = -6 and gave an answer of 2. What might the student have done wrong? Explain. Then give the correct answer. 21. Explain the different ways it is possible to add two integers and get a negative answer.
22. The temperature rose from -4ºF to 45ºF in Spearfish, South Dakota, on January 22, 1943, in only 2 minutes! By how many degrees did the temperature change? 23. A submarine cruising at 27m below sea level, or -27m, descends 14m. What is its new depth? 24. A roller coaster starts with a 160-foot climb and then plunges 228 feet down a canyon wall. It then climbs a gradual 72 feet before a steep climb of 189 feet. Approximately how far is the coaster above or below its starting point? 25. If you know that the product of two integers is negative, what can you say about the two integers? Give examples. 26. A visiting player is positioned on his own 30-yard line. The player loses 3 yards after a gain of 12 yards. What is the player s position if 4 yards are lost on each of the next two plays? 27. Brenda donates part of her salary to the local children s hospital each month by having $15 taken out of her monthly paycheck. Write an integer to represent the amount taken out of each paycheck. Find the integer to represent the change in the amount of money in Brenda s paychecks after 1.5 years. (For #28-29) An investor buys shares of Stock A and Stock B. Stock A loses $8 per share, and Stock B gains $5 per share. Given the number of shares, how much does the investor lose or gain? 28. Stock A: 20 shares, Stock B: 35 shares 29. Stock A: 30 shares, Stock B: 20 shares (For #30-31) A student puts $50 in the bank each time he makes a deposit. He takes $20 each time he makes a withdrawal. Given the number of transactions, what is the net change in the students account? 30. deposits: 4, withdrawals: 5 31. deposits: 3, withdrawals: 8
32. A team of mountain climbers descended 3,600 feet to a camp that was at an altitude of 12,035 feet. At what altitude did they start? 33. Olivia owns 43 CDs. This is 15 more CDs than April owns. How may CDs does April own? 34. In 1990, the population of Cheyenne, Wyoming, was 73,142. By 2000, the population had increased to 81,607. Write and solve an equation to find n, the increase in Cheyenne s population from 1990 to 2000. 35. An ion is a charge particle. Each proton in an ion has a charge of +1 and each electron has a charge of -1. The ion charge is the electron charge plus the proton charge. Write and solve an equation to find the electron change for each ion. Name of Ion Proton Charge Electron Charge Ion Charge Aluminum ion +13 +3 Hydroxide ion +9-1 Oxide ion +8-2 Sodium ion +11 +1 36. Explain, in words, how you could solve for h in the equation 14 h = 8 using Algebra. Then use your method to solve for the value of h. 37. A kilowatt-hour is one kilowatt of power that is supplied for one hour. The lighting for a 3-hour concert uses a total of 210 kilowatt-hours of electricity. How many kilowatts of electricity do the lights require? 38. One serving of milk contains 8 grams of protein, and one serving of steak contains 32 grams of protein. Write and solve an equation to find the number of servings of milk m needed to get the same amount of protein as there is in one serving of steak. x 39. Will the solution of 11 5 be greater than 11 or less than 11? Explain how you know. 40. Joy earns $8 per hour at an after-school job. Each month she earns $128. How many hours does she work each month? After six months, she gets a $2 per hour raise. How much money does she earn per month now? 41. While on vacation Milo drove his car a total of 370 miles. This was 5 times as many miles as he drives in a normal week. How many miles does Milo drive in a normal week?
42. In the equation ax = 12, a is an integer. Is it possible to choose a value of a so that the solution of the equation is x = 0? Why or why not? 43. Jason wants to buy a trumpet advertised for $195. He has saved $156. Using the information, write and solve an equation to find how much more money he needs to buy the trumpet. 44. Write a problem that can be solved using the equation 15x = 75. What is the solution of the problem? m 45. Explain how to estimate the solution of 97. 8 46. During a winter storm, the temperature dropped -3ºF every hour. The overall change in the temperate was -18ºF. Write and solve an equation to determine how long the storm lasted. 47. A website that rents DVDs charges a one-time fee of $7 to become a member of the site. It costs $3 to rent each DVD. Diana joined the site and spent a total of $61. How many DVDs did she rent? Write and solve a 2-step equation. 48. Bob s Auto Shop charges $375 to replace the timing belt in a car. The belt costs $50 and the labor to install the belt costs $65 per hour. How many hours does it take to install the timing belt? Write and solve a 2-step equation. 49. Mike has 60 baseball cards in his collection. Each week he buys a pack of cards to add to the collection. Each pack contains the same number of cards. After 12 weeks, Mike has 156 cards. Write and solve an equation to find the number of cards in a pack. 50. In 1956, during President Eisenhower s term, construction began on the United States interstate highway system. The original plan was for 42,000 miles of highways to be completed within 16 years. It actually took 37 years to complete! The last part was completed in 1993. Write and solve an equation to show how many miles m needed to be completed per year for 42,000 miles of highways to be built in 16 years. 51. Explain how you decide which operation to use first when solving a 2-step equation. 52. Little Johnny is in 2 nd grade and he is very curious! He would like to know how to solve the equation 5 7x = 16. Write him a letter describing the process step-by-step so that Little Johnny will be able to solve the problem.