Question

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

Shonda has ( x )dollars in her piggy bank.

Rizzo has ( x-1.50 )

if Shonda has $9 more than x; (x+9),would be equal to

3 times the dollars Rizzo has, or, 3(x-1.50). The two quantities are equal, we can solve for x.

x+9 = 3(x-1.50)

Dustribute the 3

x+9 = 3x - 4.50

Isolate the variable on the left and constants on the right of the equation by subtracting 3x and 9 from both sides.

x+9 = 3x - 4.50

-3x-9 = -3x - 9

-2x = - 13.50

Divide both sides by - 2

Shonda has; x = 6.75

Rizzo has; (6.75 - 1.50) = 5.25

6.75 + 9 = 3(6.75 - 1.50)

15.75 = 3(5.25) or 15.75.

Passes the check.

Shonda has $6.75 in her piggy bank and Rizzo has $5.25.