Solving Systems of Equations by Graphing with Word Problems

Habiba sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Ruth 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

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• (35, 52)

• (18, 69)

• ( 52, 35) 

• (61, 26)

The senior class at Orchard Collegiate High School rented and filled 11 vans and 3 buses with 283 students. The senior class at Essex High School rented and filled 12 vans and 14 buses with 770 students. How many students were on each van and each bus?

• Van 43
  Bus 14

• Van 11
  Bus 21

• Van 14
  Bus 43

• Van 17
  Bus 45

On the first night, the Movie House Theater sold 7 adult tickets and 11 child tickets for $227. On the second night they took in $150 by selling 6 adult tickets and 6 child tickets. Find the price of an adult ticket and the price of a child ticket.

• Adult $13
  Child $5

• Adult $10
  Child $6

• Adult $8
  Child $16

• Adult $12
  Child $13

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740

• S + A = 530
  4S + 3A = 1740

• S + A = 1740
  3S + 4A = 530

• S + A = 1740
  4S + 3A = 530

Yazzy 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 Yazzy 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

Dishann 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. Which system of equations could be used to find the exact number of dimes and nickels?

• d + n = 6.60
  .10d + .05n = 80

• d + n = 80
  d + n = 6.60

• d + n = 80
  .10d + .05n = 6.60

• d + n = 80
  .05d + .10n = 6.60

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 customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $68 for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450

• 3x + 2y = 450
  2x + 4y = 315

• 2x + 2y = 315
  3x + 4y = 450