40% of Lucy's amount was $413 less than Flynn's amount. When Lucy spent 25% of her amount and Flynn spent 60% of his amount, they had the same amount of amount left. Find the amount that Flynn had at first.

	Lucy	Flynn
Before	8 u	15 u
Change	- 2 u	- 9 u
After	6 u	6 u

Percentage of Lucy's amount left
= 100% - 25%
= 75%

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

75% = ⁷⁵₁₀₀ = ³₄
40% = ⁴⁰₁₀₀ = ²₅

The amounts of amount that Lucy and Flynn had left were the same. Make the numerators the same.

³₄ of Lucy's amount = ²₅ of Flynn's amount
⁶₈ of Lucy's amount = ⁶₁₅ of Flynn's amount

Amount that Lucy had = 8 u

40% of the amount that Lucy had
= 40% x 8 u
= ⁴⁰₁₀₀ x 8 u
= 3.2 u

Difference between Flynn's amount and 40% of Lucy's amount
= 15 u - 3.2 u
= 11.8 u

11.8 u = 413

1 u = 413 ÷ 11.8 = 35

Amount that Flynn had at first
= 15 u
= 15 x 35
= $525

Answer(s): $525