70% of Penelope's amount was $42 more than Luke's amount. When Penelope spent 55% of her amount and Luke spent 35% of his amount, they had the same amount of amount left. Find the amount that Luke had at first.

	70% of Penelope's amount	Penelope's amount	Luke's amount
Before	182 u	260 u	180 u
Change		- 143 u (- 55%)	- 63 u (- 35%)
After		117 u	117 u

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

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

45% = ⁴⁵₁₀₀ = ⁹₂₀
65% = ⁶⁵₁₀₀ = ¹³₂₀

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

⁹₂₀ of Penelope's amount = ¹³₂₀ of Luke's amount
¹¹⁷₂₆₀ of Penelope's amount = ¹¹⁷₁₈₀ of Luke's amount

Amount that Penelope had = 260 u

70% of the amount that Penelope had
= 260 u x 70%
= 260 u x ⁷⁰₁₀₀
= 182 u

Difference between 70% of Penelope's amount and Luke's amount
= 182 u - 180 u 
= 2 u

2 u = 42
1 u = 42 ÷ 2 = 21

Amount that Luke had at first
= 180 u
= 180 x 21
= $3780

Answer(s): $3780