Usha had $646 less than Dylan. Usha spent ¹₆ of her money and Dylan spent ⁴₇ of his money. In the end, Dylan and Usha had the same amount of money left. Find the amount of money Dylan had at first.

	Usha	Dylan	Difference
Before	6x3 = 18 u	7x5 = 35 u	17 u
Change	- 1x3 = - 3 u	- 4x5 = - 20 u
After	5x3 = 15 u	3x5 = 15 u

Fraction of Usha's money left
= 1 - ¹₆
= ⁵₆

Fraction of Dylan's money left
= 1 - ⁴₇
= ³₇

Dylan and Usha had the same amount of money in the end. Make the numerators the same. LCM of 5 and 3 is 15.

⁵₆ of Usha's money = ³₇ of Dylan's money
¹⁵₁₈ of Usha's money = ¹⁵₃₅ of Dylan's money

Amount that Usha had at first = 18 u
Amount that Dylan had at first = 35 u

Amount that Usha had less than Dylan had at first
= 35 u - 18 u
= 17 u

17 u = 646

1 u = 646 ÷ 17 = 38

Amount that Dylan had at first
= 35 u
= 35 x 38
= $1330

Answer(s): $1330