Generate Expressions 1. If a coffee company purchases paper cups at a cost of x cents for a package of ten and lids at a cost of y cents per dozen, which of the following represents its material cost, in cents, of c cups of coffee? 2. If a car rental company charges $100 for each rental, a dollars per mile, and b dollars per hour, which of the following represents the total cost to rent a car for 6 hours and travel 250 miles? 100 + 250a + 6b 3.
In a library there are currently B bookshelves, each with 40 books.
C new bookshelves are added, then 5 books are added to every bookshelf in the library. How many books have been added to the library? 45C + 5B 4. A boat drifts down a 200-mile river at a rate of 6 miles per hour for the first h hours. In terms of h, where h < 30, how many miles remain to be traveled? 200-6h 5. If Sarah earns d dollars per hour for babysitting, and t dollars per hour of travel time, which of the following represents her earnings after babysitting for 4 hours and traveling one hour to the family’s house? 4d+t 6. The cost of a pair of shoes is S dollars.
If the shoes go on sale for P percent off of their original price, and Joey buys them with a coupon for an additional C percent off of the sale price, then what price does Joey pay? | | | | 7. If Peter can mow the front lawn in 15 minutes less than twice the time it takes Amanda to mow the lawn, and Amanda can mow the lawn in h hours, which of the following expressions represents the time in hours it takes Peter to mow the lawn? 8h – 1| | 4| 8. Joe can ride his bike M miles in 1 hour. If he lives 3 miles from school and it takes him N minutes to get there, which of the following represents M in terms of N? 80| | N| 9. If each support cable can support p pounds, and the total weight of an elevator is m pounds, which of the following represents the number of cables required to support the elevator? m/p 10. If Kat is four years more than twice as old as Andrew, and Kat is a years old, which of the following expressions represents the age of Andrew? 11. If Rick takes 10 seconds more than two-thirds the time it takes Ted to run the 400 meter dash, and Rick runs the 400 meter dash in s seconds, which of the following expressions represents the time it takes Ted to run the 400 meter dash? 2. The original price of for a meal is p dollars. During lunch, however, the restaurant offers a discount of x percent. Janet also uses a coupon that offers y dollars off the discounted price. Which of the following represents the price, in dollars, that Janet paid for the meal? 13. A flagpole twelve feet tall casts a shadow two feet long. If Jill is standing next to the flagpole and casts a shadow that is x inches long, how tall is Jill, in feet? 14. A repairman charges f for the first hour of work and d dollars for each additional hour.
If he earns $445 working one job, and he is there for more than one hour, which of the following expressions represents the time he spent at the job? 15. If the average (arithmetic mean) of the 3 numbers above is 3y, what is x in terms of y? y 16. An apple orchard has n trees, and each tree typically produces a apples in a season. If the orchard plants m additional trees, in terms of a, n and m, what will be the expected total yield of apples? am + an 17. If the average (arithmetic mean) of w + 2 and 3w is y and the average of 3w – 4 and w is x, what is the average of x and y? 2w – ? 8. A laptop battery, when fully charged, can power a computer for h hours. The battery takes j minutes to fully charge. If the battery charged for k minutes, and k ; j, which of the following represents the amount of time, in hours, the battery can power the computer? 19. Susan is paid m dollars per hour for the f hours she works at the local record store. If she works more than f hours a week, Susan is paid an additional k dollars per hour for each additional hour. If Susan works a total of h hours in a week, and h ; f, in terms of m, f, k and h, what is Susan paid for the week? m + hk – kf 20. Derek and Pete are all paid hourly for their work at the local coffee shop. Derek is paid 10 dollars per hour, which is a dollars per hour more than Pete. Derek also works 37 hours each week, which is b hours less than Pete. If Pete earns c dollars in a week, what is a in terms of b and c? 21. The average (arithmetic mean) of three numbers is 2x. If one of the numbers is y + 3, what is the average of the remaining two numbers in terms of x and y? 22. An auditorium originally has 30 chairs per row and a total of 25 rows.
The auditorium undergoes renovations so that each of the rows is extended by c chairs, and an additional r rows are added. In terms of r and c, how many additional chairs have been added? (30 + c)(25 + r) – 750 23. If Lisa’s phone company charges ten cents per minute for phone calls and fifteen cents for each text message, which of the following represents the total bill (in dollars) due to the phone company if Lisa talked for m minutes and sent t texts? 0. 10m + 0. 15t 24. A taxi service charges a base fare of d dollars, and then an additional b dollars per quarter-mile. If the total fare was $11. 5, which of the following represents the total distance traveled? 25. Each box of cupcakes costs f dollars to produce and contains c cupcakes. Each cupcake is sold for d dollars. What is the profit from selling a box of cupcakes? Cd-f 26. A new hybrid car can travel t miles per gallon, and the gas tank can hold g gallons of gas. If gas costs $2 per gallon, which of the following represents the cost, in dollars, required to travel one mile? 2/t 27. If Tom is seven years less than twice as old as Rick, and Rick is n years old, which of the following expressions represents the age of Tom? n – 7 28. Which of the following represents the total cost, in dollars, if Sally bought 8 apples which cost n dollars each and 6 oranges which each cost half as much as an apple? 11n 29. The original price of a CD was d dollars, but it was discounted x percent during a seasonal sale. If the sales tax of y percent was applied to the sale price, which of the following represents the price, in dollars, of the CD? | 30. Jen, Liz and Radha decided to take a road trip across the country. Jen drove a total of j miles.
Liz drove 100 miles less than twice as many miles as Jen drove, and Radha drove half as many miles as Liz. In terms of j, what was the average miles each person drove? 31. Which of the following represents the total cost, in dollars, of y yards of yarn at 2 dollars per foot, and b buttons at 40 cents per button? (1 yard = 3 feet) 6y + 0. 4b 32. Which of the following represents the total cost in dollars for x hot dog buns and y hot dogs if buns cost $7 per dozen and hot dogs cost fifty cents each? 33. Which of the following represents the area of the figure shown above? (a – c – b) + 1/2(c + b)2 34. The average (arithmetic mean) of three numbers is x. If one of the numbers is 2y – 1, what is the average of the remaining two numbers in terms of x and y? S and T are consecutive even integers with T > S. S is what percent of T? | | 35. A car rental company charges r dollars for the first hour and then it charges any additional hours at a rate of s dollars per hour. If the total cost for a rental is t dollars and the rental lasts longer than one hour, which of the following expressions represents the length of the rental in hours? t – r + s| s| 36. There are x coins in a jar. If one coin is to be selected at random, the probability that a penny will be selected randomly is 2/5 and the probability that a nickel will be selected randomly is 1/4. In terms of x, how many coins are neither pennies nor nickels? 37. A swimming pool can hold y gallons at maximum capacity. If a hose can fill the pool at a rate of x gallons per second, which of the following expressions represents the time, in minutes, to fill an empty swimming pool to 90% capacity? 38. Lisa, Sally and Jessica all sold lemonade outside of their houses.
Lisa sold k cups of lemonade. Sally sold five cups less than twice as many cups of lemonade as Lisa, and Jessica sold nine cups more than three times the number of cups that Sally sold. In terms of k, how many cups of lemonade did Jessica sell? 6k – 6 39. The average of 2 numbers is A. When a third number is included, the average becomes B. What is the third number in terms of A and B? 3B – 2A 40. In a six-hour flight from New York to Los Angeles, an airplane averages 200 miles per hour during the first t hours until it reaches cruising altitude.
Once at the cruising altitude, the airplane travels at 545 miles per hour for the remainder of the trip. If terms of t, where t < 6, how far is the flight? 545 ? 6 – 345t 41. If the steps above are followed in order, which of the following is a simplified expression for the result? -7y + 11x 42. Jacob wants to buy new school supplies. If pens cost 75 cents each and notebooks cost 2 dollars each, which of the following represents the cost, in dollars, of p pens and n notebooks? 43. The force exerted on an object is defined as the product of the mass of the object and its acceleration. The force exerted on a ball is initially f.
If the mass of the ball remains the same but the acceleration decreases by a factor of three, what is the resulting force on the ball? 44. The original price of a pair of pants was p dollars but they were discounted x percent during a seasonal sale. If the sales tax of y percent was applied to the discounted price, which of the following represents the price, in dollars, of the pants? 45. A hotdog stand buys hot dogs by the carton. Each carton has p packages of hot dogs, and each package contains h hot dogs. If each carton of hot dogs costs c dollars, what is the cost per hot dog? c/ph 46.