Solving Systems of Equations by Graphing with Word Problems

A vending machine has nickels and dimes. The vending machine has 32 coins in total, with a value of $2.60. What equation models the scenario?

• n + d = 32

  .05n + .10d = 2.60

• n + d = 2.60

  .05n + .10d = 32

• n + d = 32

  .10n + .25d = 2.60

• n + d = 2.60

  .10n + .25d = 32

A piggy bank has dimes and quarters. The piggy bank has 25 coins, and has a value of $4.90. What system of equations models this scenario?

• d + q = 25

  .10d + .25q = 4.90

• d + q = 4.90

  .10d + .25q = 25

• d + q = 25

  .05d + .10q = 4.90

• d + q = 4.90

  .05d + .10q = 25

You sell 15 rolls of wrapping paper for a fundraiser.  Shiny wrapping paper costs $4 and regular wrapping paper costs $2. The total for the 15 rolls was $44.  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

What is the solution to this system of equations?

• (1,4)

• (4,1)

• (3,5)

• (-1, 4)

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. To solve, I graphed: x + y = 21 6x + 4y = 104 I got an intersection point at (10,11). What does that mean in context of the problem?

• There are 10 adults and 11 children.

• There are 11 adults and 10 children.

• The adults are $10 and the children are $11.

• There are 104 adults and 21 children.

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer 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

The brown bunny (x) ate 22 carrots more than the white bunny (y). The bunnies together had eaten a total of 60 carrots during the week. How many carrots did each bunny eat?

• x + y = 22

  x = y + 60

• x + y = 60

  x = y + 22

• x + y = 22

  y = x - 22

• 2x + y = 22

  x = y + 60

Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular. One night, the theater sells 578 tickets and collects $3365 in total ticket sales.
Which system best represents the situation?

• 4x + 7y = 578
  x + y = 3365

• 4x + 7y = 3365
  x + y = 578

• 4y + 7x = 578
  x + y = 3365

• 4y + 7x = 3365
  x + y = 578

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

• x + y = 33
  y = 2x - 3

• x + y = 33
  x = 2y - 3

• x + y = 33
  x = 3 - 2y

• x + y = 3
  x = 33 - 2y

Two small pitchers and one large pitcher can hold 8 cups of water.  One large pitcher minus one small pitcher constitutes 2 cups of water.  How many cups of water can each pitcher hold?

• 8 large, 2 small

• 6 large, 4 small

• 4 large, 2 small

• 2 large, 2 small