90% of Vanessa's amount was $432 more than Peter's amount. When Vanessa spent 55% of her amount and Peter spent 20% of his amount, they had the same amount of amount left. Find the amount that Peter had at first.

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

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

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

45% = ⁴⁵₁₀₀ = ⁹₂₀
80% = ⁸⁰₁₀₀ = ⁴₅

The amounts of amount that Vanessa and Peter had left were the same.
Make the numerators the same.

⁹₂₀ of Vanessa's amount = ⁴₅ of Peter's amount
³⁶₈₀ of Vanessa's amount = ³⁶₄₅ of Peter's amount

Amount that Vanessa had = 80 u

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

Difference between 90% of Vanessa's amount and Peter's amount
= 72 u - 45 u 
= 27 u

27 u = 432
1 u = 432 ÷ 27 = 16

Amount that Peter had at first
= 45 u
= 45 x 16
= $720

Answer(s): $720