80% of Cathy's amount was $380 more than Harry's amount. When Cathy spent 55% of her amount and Harry spent 20% of his amount, they had the same amount of amount left. Find the amount that Harry had at first.

	80% of Cathy's amount	Cathy's amount	Harry's amount
Before	64 u	80 u	45 u
Change		- 44 u (- 55%)	- 9 u (- 20%)
After		36 u	36 u

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

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

45% = ⁴⁵₁₀₀ = ⁹₂₀
80% = ⁸⁰₁₀₀ = ⁴₅

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

⁹₂₀ of Cathy's amount = ⁴₅ of Harry's amount
³⁶₈₀ of Cathy's amount = ³⁶₄₅ of Harry's amount

Amount that Cathy had = 80 u

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

Difference between 80% of Cathy's amount and Harry's amount
= 64 u - 45 u 
= 19 u

19 u = 380
1 u = 380 ÷ 19 = 20

Amount that Harry had at first
= 45 u
= 45 x 20
= $900

Answer(s): $900