Penelope had $216 less than Oliver. Penelope spent ¹₇ of her money and Oliver spent ³₅ of his money. In the end, Oliver and Penelope had the same amount of money left. Find the amount of money Oliver had at first.

	Penelope	Oliver	Difference
Before	7x1 = 7 u	5x3 = 15 u	8 u
Change	- 1x1 = - 1 u	- 3x3 = - 9 u
After	6x1 = 6 u	2x3 = 6 u

Fraction of Penelope's money left
= 1 - ¹₇
= ⁶₇

Fraction of Oliver's money left
= 1 - ³₅
= ²₅

Oliver and Penelope had the same amount of money in the end. Make the numerators the same. LCM of 6 and 2 is 6.

⁶₇ of Penelope's money = ²₅ of Oliver's money
⁶₇ of Penelope's money = ⁶₁₅ of Oliver's money

Amount that Penelope had at first = 7 u
Amount that Oliver had at first = 15 u

Amount that Penelope had less than Oliver had at first
= 15 u - 7 u
= 8 u

8 u = 216

1 u = 216 ÷ 8 = 27

Amount that Oliver had at first
= 15 u
= 15 x 27
= $405

Answer(s): $405