Solving Word Problems Using Variables

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have?  Which system best represents the situation? 

• x + y = 1430
  20x + 50y = 49

• x + y = 49
  10x + 5y = 1430 

• x + y = 49
  20x + 50y = 1430

• x + y = 49
  x + y = 1430

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38
  2s + 3c = 52

• 3s + 1c = 38
  3s + 2c = 52

• s + c = 38
  s + c = 52

• 3s + 3c = 38
  1s + 2c = 52

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

• 10c + 5d = 14.25
  5c + 10d = 16.50

• 10c + 5d = 16.50
  5c + 10d = 14.25

• c + d = 10
  5c + 10d = 16.50

• c + d = 5
  5c + 10d = 16.50

Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?

• $5

• $10

• $15

• $20

A business that rents cars is open for 8 hours on Monday. On Monday morning the business had 45 cars. The business rented 3 cars to customers during each of the first 5 hours. The business rented 2 cars to customers during each of the next 3 hours. The total number of cars that were brought back to the business by customers on Monday was 17. In which equation does c represent the number of cars the business had at the end of the day on Monday?

• c = 45−(5+3)−(3+2)+17

• c = 45−(5×3)−(3×2)−17

• c = 45−(5+3)−(3+2)−17

• c = 45−(5×3)−(3×2)+17

A business that rents cars is open for 8 hours on Monday. On Monday morning the business had 45 cars. The business rented 3 cars to customers during each of the first 5 hours. The business rented 2 cars to customers during each of the next 3 hours. The total number of cars that were brought back to the business by customers on Monday was 17. In which equation does c represent the number of cars the business had at the end of the day on Monday?

• 0. c = 45−(5+3)−(3+2)+17

• 0. c = 45−(5×3)−(3×2)−17

• 0. c = 45−(5+3)−(3+2)−17

• 0. c = 45−(5×3)−(3×2)+17

For a conference, a hotel charges $45 per hour for the use of a banquet room, plus $22.95 per person. What is the total cost to rent a banquet room for 3 hours for 180 people?

• $337.95

• $1572.75

• $4266.00

• $8168.85

The sum of Mr. Micklow and Ms. Craft's age is 55.  The difference is 3.  
Solve:
x + y = 55
x - y = 3

• (26, 23)

• (26, 29)

• (29, 26)

• (29, 32)

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

• Sugar Cookies $5 
  Oatmeal Cookies $3

• Sugar Cookies $4
  Oatmeal Cookies $8

• Sugar Cookies $2
  Oatmeal Cookies $6

• Sugar Cookies $3
  Oatmeal Cookies $6

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all.  Upon completing the job he counted out the coins and it came to $6.60.  How many nickels and dimes did Dennis earn? 

• 40 nickels, 40 dimes

• 52 nickels, 28 dimes

• 28 nickels, 52 dimes

• 30 nickels, 50 dimes