Carnegie Writing and Solving Equations

Pilar had brochures printed for a new business venture. Pilar originally ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures, which cost a total of $134. After those ran out, Pilar spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?

• x+y=134

  x+y=120

• 3x+3y=134

  4x+3y=120

• 4x+3y=134

  3x+3y=120

• 7xy=134

  6xy=120

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

Saulo 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, Saulo made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• 1.5x+0.5y=78.5

  x+y=87

• 1.5x+0.5y=78.5

  1.5x+0.5y=87

• x+y=78.5

  1.5x+0.5y=87

• x+y=78.5

  x+y=87

What is the solution?

• (1, -1)
• (-1, 1)
• (0, -2)
• (2, 0)

How many solutions will this system have? 

• No solution
• One Solution
• I Don't Know
• Infinitely Many Solutions

Tania had 35 coins in pennies and nickels. She had $1.03. Which system of equations could be used to determine the number of coins she has?

• .01p + .05n = 35

  p + n = 103

• 1p + 5n = 1.03

  p + n = 35

• .01p + .05n = 1.03

  p + n = 35

• .05p + .01n = 1.03

  p + n = 35

Write a system of equation to solve the following situation.

Two groups of people order food at a restaurant. one group order 4 pizzas and 7 salads for $34.50. The other group orders 8 pizzas and 3 salads for $30.50. Find the cost of each item.

Let p = pizza and s = salad.

• 4p +7s = 30.50 and 8p + 3s = 34.50

  A pizza costs $2. 40 and a salad costs $3.40

• 4p +7s = 34.50 and 8p + 3s = 30.50

  A pizza costs $2. 50 and a salad costs $3.50

• 4p -7s = 34.50 and 8p - 3s = 30.50

  A pizza costs $1.50 and a salad costs $4.50

• 4p +7s = 34.50 and 8p + 3s = 30.50

  A pizza costs $3.50 and a salad costs $2.50

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.  After solving the system below, Alexandra gets a solution of (45,90)

3x + 2y = 315

2x + 4y = 450

What does the solution (45,90) mean?

• Hair dyes take Alexandra 45 minutes & haircuts take 90 minutes.

• Haircuts take Alexandra 45 minutes & hair dyes take 90 minutes.

• Haircuts cost $45 & hair dyes cost $90.

• Hair dyes cost $45 & haircuts cost $90.