80% of Emma's amount was $464 more than Liam's amount. When Emma spent 65% of her amount and Liam spent 20% of his amount, they had the same amount of amount left. Find the amount that Liam had at first.

	80% of Emma's amount	Emma's amount	Liam's amount
Before	64 u	80 u	35 u
Change		- 52 u (- 65%)	- 7 u (- 20%)
After		28 u	28 u

Percentage of Emma's amount left
= 100% - 65%
= 35%

Percentage of Liam's amount left
= 100% - 20%
= 80%

35% = ³⁵₁₀₀ = ⁷₂₀
80% = ⁸⁰₁₀₀ = ⁴₅

The amounts of amount that Emma and Liam had left were the same.
Make the numerators the same.

⁷₂₀ of Emma's amount = ⁴₅ of Liam's amount
²⁸₈₀ of Emma's amount = ²⁸₃₅ of Liam's amount

Amount that Emma had = 80 u

80% of the amount that Emma had
= 80 u x 80%
= 80 u x ⁸⁰₁₀₀
= 64 u

Difference between 80% of Emma's amount and Liam's amount
= 64 u - 35 u 
= 29 u

29 u = 464
1 u = 464 ÷ 29 = 16

Amount that Liam had at first
= 35 u
= 35 x 16
= $560

Answer(s): $560