William had $37.5 and Gracie had $52.5 in the beginning
Step-by-step explanation:
William says to Gracie:
Grace responds:
Assume that William has $x and Gracie has $y at the beginning
∵ William has $x
∵ Gracie has $y
∵ When Gracie gives William $7.5, they will have the same
amount of money
- That means subtract 7.5 from Gracie and add 7.5 to William
and equate the two answers
∴ x + 7.5 = y - 7.5
- Subtract 7.5 from both sides
∴ x = y - 15 ⇒ (1)
∵ When William gives Gracie $7.5, Gracie will have twice as
much money as William
- That means add 7.5 to Gracie and equate the sum
by 2 times the difference of William and 7.5
∴ y + 7.5 = 2(x - 7.5)
∴ y + 7.5 = 2x - 15
- Subtract 7.5 from both sides
∴ y = 2x - 22.5 ⇒ (2)
Now we have system of equations to solve it
Substitute y in equation (1) by equation (2)
∵ x = 2x - 22.5 - 15
- Add the like terms in the right hand side
∴ x = 2x - 37.5
- Subtract 2x from both sides
∴ - x = -37.5
- Divide both sides by -1
∴ x = 37.5
- Substitute the value of x in equation (2) to find y
∵ y = 2(37.5) - 22.5
∴ y = 52.5
William had $37.5 and Gracie had $52.5 in the beginning
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
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