50% of Cathy's amount was $320 less than Peter's amount. When Cathy spent 40% of her amount and Peter spent 60% of his amount, they had the same amount of amount left. Find the amount that Peter had at first.

	Cathy	Peter
Before	10 u	15 u
Change	- 4 u	- 9 u
After	6 u	6 u

Percentage of Cathy's amount left
= 100% - 40%
= 60%

Percentage of Peter's amount left
= 100% - 60%
= 40%

60% = ⁶⁰₁₀₀ = ³₅
40% = ⁴⁰₁₀₀ = ²₅

The amounts of amount that Cathy and Peter had left were the same. Make the numerators the same.

³₅ of Cathy's amount = ²₅ of Peter's amount
⁶₁₀ of Cathy's amount = ⁶₁₅ of Peter's amount

Amount that Cathy had = 10 u

50% of the amount that Cathy had
= 50% x 10 u
= ⁵⁰₁₀₀ x 10 u
= 5 u

Difference between Peter's amount and 50% of Cathy's amount
= 15 u - 5 u
= 10 u

10 u = 320

1 u = 320 ÷ 10 = 32

Amount that Peter had at first
= 15 u
= 15 x 32
= $480

Answer(s): $480