Question

1. Write a system of equations to describe the situation. Then solve the system. Be sure to define your variables! Rizzo has $1.50 less in his piggy bank than his sister Shonda. If Shonda had $9 more, she would have three times as much money as Rizzo. How much money do each of the children have in their banks?

Answer 1

The amount Rizzo has = x = $5.25

The amount Shonda has = y = $6.75

Explanation:

Let us represent:

The amount Rizzo has = x

The amount Shonda has = y

Rizzo has $1.50 less in his piggy bank than his sister Shonda.

x = y - 1.50.......Equation 1

If Shonda had $9 more, she would have three times as much money as Rizzo.

y + 9 = 3(x)

y + 9 = 3x..... Equation 2

y = 3x - 9

We substitute 3x - 9 for y in Equation 1

x = y - 1.50.......Equation 1

x = 3x - 9 - 1.50

9 + 1.50 = 3x - x

10.50 = 2x

x = 10.50/2

x = $5.25

Solving for y

y = 3x - 9

y = 3(5.25) - 9

y = $6.75

Therefore:

The amount Rizzo has = x = $5.25

The amount Shonda has = y = $6.75