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Interpreting Equations in Context

1.10.1 Interpreting Equations in Context

1.10.1 • Interpreting Equations in Context

Warm Up

A vibrant nighttime carnival scene with colorful lights, a glowing Ferris wheel, game booths like Balloon Pop, hanging prizes, and a crowd of people enjoying the festive atmosphere.

Jada has $20 to spend on games and rides at a carnival.

  • Games cost $1 each.
  • Rides are $2 each.

In the following activity, you will complete a series of questions regarding this scenario.

1. Which equation represents the relationship between the number of games, xx, and the number of rides, yy, Jada could do if she spends all $20?

  1. x + y = 20 x + y = 20
  2. 2 x + y = 20 2 x + y = 20
  3. x + 2 y = 20 x + 2 y = 20

x + 2 y = 20 x + 2 y = 20

2. Explain what each of the other two equations could mean in this situation.

Your answer may vary, but here are some samples.

In this situation, the equation x + y = 20 x + y = 20 could mean:

  • Jada spends $20 on games and rides that cost $1 each.
  • The combined number of games and rides that Jada enjoys is 20.

In this situation, the equation 2 x + y = 20 2 x + y = 20 could mean:

  • Jada spends $20 on games and rides, where games cost $2 each and rides are $1 each.