Question

A set of two or more equations with the same variables is called a system of equations. When you set the

two expressions that are equal to the same variable equal to each other, like you did in the previous lesson,
you are using the Equal Values Method of solving a system of equations. Use the Equal Values Method to
solve the following problem.
It is time to cool off on a hot summer day! Team Sunshine is filling an inflatable kiddie pool from a garden
hose. The pool has 30 gallons in it and Team Sunshine is adding 8 gallons per minute with a garden hose.
Next door, Team Breeze's pool is already filled with 180 gallons of water. They are emptying the pool at 5
gallons per minute with buckets.
Write two equations to represent the situation. Use the equations to find how long it takes until both pools
have the same amount of water. Check your calculations.

Answer 1

Both pools will have the same amount of water after 11 minutes and 32 seconds.

Explanation:

Since Team Sunshine is filling an inflatable kiddie pool from a garden hose, and the pool has 30 gallons in it and Team Sunshine is adding 8 gallons per minute with a garden hose, while next door, Team Breeze's pool is already filled with 180 gallons of water, and they are emptying the pool at 5 gallons per minute with buckets, to determine how long it will take until both pools have the same amount of water, the following calculation must be performed:

Team Sunshine:

30 + (8X) = T

30 + 8x10 = 110

30 + 8x11 = 118

30 + 8x12 = 126

30 + 8x11.5 = 122

30 + 8x11.6 = 122.8

30 + 8x11.55 = 122.4

30 + 8x11.54 = 122.3

Team Breeze:

180 - (5X) = T

180 - 5x11 = 125

180 - 5x12 = 120

180 - 5x11.5 = 122.5

180 - 5x11.6 = 122

180 - 5x11.55 = 122.25

180 - 5x11.54 = 122.3

1 = 60

0.54 = X

0.54 x 60 = X

32.4

Thus, both pools will have the same amount of water after 11 minutes and 32 seconds.