40% of Zara's amount was $1209 less than Luke's amount. When Zara spent 45% of her amount and Luke spent 60% of his amount, they had the same amount of amount left. Find the amount that Luke had at first.

	Zara	Luke
Before	40 u	55 u
Change	- 18 u	- 33 u
After	22 u	22 u

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

Percentage of Luke's amount left
= 100% - 60%
= 40%

55% = ⁵⁵₁₀₀ = ¹¹₂₀
40% = ⁴⁰₁₀₀ = ²₅

The amounts of amount that Zara and Luke had left were the same. Make the numerators the same.

¹¹₂₀ of Zara's amount = ²₅ of Luke's amount
²²₄₀ of Zara's amount = ²²₅₅ of Luke's amount

Amount that Zara had = 40 u

40% of the amount that Zara had
= 40% x 40 u
= ⁴⁰₁₀₀ x 40 u
= 16 u

Difference between Luke's amount and 40% of Zara's amount
= 55 u - 16 u
= 39 u

39 u = 1209

1 u = 1209 ÷ 39 = 31

Amount that Luke had at first
= 55 u
= 55 x 31
= $1705

Answer(s): $1705