30% of Gem's amount was $600 less than Cole's amount. When Gem spent 40% of her amount and Cole spent 60% of his amount, they had the same amount of amount left. Find the amount that Cole had at first.

	Gem	Cole
Before	10 u	15 u
Change	- 4 u	- 9 u
After	6 u	6 u

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

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

60% = ⁶⁰₁₀₀ = ³₅
40% = ⁴⁰₁₀₀ = ²₅

The amounts of amount that Gem and Cole had left were the same. Make the numerators the same.

³₅ of Gem's amount = ²₅ of Cole's amount
⁶₁₀ of Gem's amount = ⁶₁₅ of Cole's amount

Amount that Gem had = 10 u

30% of the amount that Gem had
= 30% x 10 u
= ³⁰₁₀₀ x 10 u
= 3 u

Difference between Cole's amount and 30% of Gem's amount
= 15 u - 3 u
= 12 u

12 u = 600

1 u = 600 ÷ 12 = 50

Amount that Cole had at first
= 15 u
= 15 x 50
= $750

Answer(s): $750