80% of Gem's amount was $280 more than Liam's amount. When Gem spent 55% of her amount and Liam spent 35% of his amount, they had the same amount of amount left. Find the amount that Liam had at first.

	80% of Gem's amount	Gem's amount	Liam's amount
Before	208 u	260 u	180 u
Change		- 143 u (- 55%)	- 63 u (- 35%)
After		117 u	117 u

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

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

45% = ⁴⁵₁₀₀ = ⁹₂₀
65% = ⁶⁵₁₀₀ = ¹³₂₀

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

⁹₂₀ of Gem's amount = ¹³₂₀ of Liam's amount
¹¹⁷₂₆₀ of Gem's amount = ¹¹⁷₁₈₀ of Liam's amount

Amount that Gem had = 260 u

80% of the amount that Gem had
= 260 u x 80%
= 260 u x ⁸⁰₁₀₀
= 208 u

Difference between 80% of Gem's amount and Liam's amount
= 208 u - 180 u 
= 28 u

28 u = 280
1 u = 280 ÷ 28 = 10

Amount that Liam had at first
= 180 u
= 180 x 10
= $1800

Answer(s): $1800