90% of Lynn's amount was $405 more than Sam's amount. When Lynn spent 55% of her amount and Sam spent 20% of his amount, they had the same amount of amount left. Find the amount that Sam had at first.

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

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

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

45% = ⁴⁵₁₀₀ = ⁹₂₀
80% = ⁸⁰₁₀₀ = ⁴₅

The amounts of amount that Lynn and Sam had left were the same.
Make the numerators the same.

⁹₂₀ of Lynn's amount = ⁴₅ of Sam's amount
³⁶₈₀ of Lynn's amount = ³⁶₄₅ of Sam's amount

Amount that Lynn had = 80 u

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

Difference between 90% of Lynn's amount and Sam's amount
= 72 u - 45 u 
= 27 u

27 u = 405
1 u = 405 ÷ 27 = 15

Amount that Sam had at first
= 45 u
= 45 x 15
= $675

Answer(s): $675