Solving Variables in Equations Word Problems

Some students want to order shirts with their school logo. One company charges a total of $9.65 per shirt plus a setup fee of $43. Another company charges a total of $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?

• y = 9.65 + x

  y = 8.40 + x

• y = 9.65x + 43

  y = 8.40x + 58

• y =9.65x

  y = 8.40x

The equations of two lines are 6x + y = 26 and y = 2x + 10. If the solution is (2, y), what is the value of y? (Hint: 1st solve the 1st equations for y, 2nd graph both equations, 3rd determine where the two lines touch. After solving, use menu 3, 2 on the N-Spire, or use the DESMOS calculator.)

• 14

• 4

• 6

Lisa and Tammy are selling items at the craft show. Which might be a reasonable solution from the graph showing the number of items sold when they both have earned the same amount? (Where will the two lines touch?)

• (1, 12)

• (3, 19)

• (5, 25)

There are 15 animals in a barn.  These animals are horses (x) and chickens (y).  There are 44 legs in all.  Which system of equations represents the situation?

• x + y = 15
  4x + 2y = 44

• 4x + 2y = 15
  x + y = 44

• x = 2y + 44
  4x = y + 15

• 2x - 4y = 44
  x - y = 15

Nancy went to the grocery story.  On Monday she purchased 4 apples (x) and 6 bananas (y) for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?

• 4x + 6y = 3
  13.5x - 13y = 6

• x + y = 4
  x - y = 6

• 4x + 6y = 13
  3x + 7y = 13.5

• 4x - 6y = 13
  3x - 7y = 13.5

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

A test has twenty questions worth 100 points.  The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each.  How many multiple choice questions are on the test?

• 20 Multiple Choice

• 10 Multiple CHoice

• 15 Multiple Choice

• 5 multiple choice