90% of Lucy's amount was $783 more than Liam's amount. When Lucy spent 55% 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.

	90% of Lucy's amount	Lucy's amount	Liam's amount
Before	72 u	80 u	45 u
Change		- 44 u (- 55%)	- 9 u (- 20%)
After		36 u	36 u

Percentage of Lucy's amount left
= 100% - 55%
= 45%

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

45% = ⁴⁵₁₀₀ = ⁹₂₀
80% = ⁸⁰₁₀₀ = ⁴₅

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

⁹₂₀ of Lucy's amount = ⁴₅ of Liam's amount
³⁶₈₀ of Lucy's amount = ³⁶₄₅ of Liam's amount

Amount that Lucy had = 80 u

90% of the amount that Lucy had
= 80 u x 90%
= 80 u x ⁹⁰₁₀₀
= 72 u

Difference between 90% of Lucy's amount and Liam's amount
= 72 u - 45 u 
= 27 u

27 u = 783
1 u = 783 ÷ 27 = 29

Amount that Liam had at first
= 45 u
= 45 x 29
= $1305

Answer(s): $1305