Xuan had $1334 less than Ahmad. Xuan spent ¹₆ of her money and Ahmad spent ⁵₇ of his money. In the end, Ahmad and Xuan had the same amount of money left. Find the amount of money Ahmad had at first.

	Xuan	Ahmad	Difference
Before	6x2 = 12 u	7x5 = 35 u	23 u
Change	- 1x2 = - 2 u	- 5x5 = - 25 u
After	5x2 = 10 u	2x5 = 10 u

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

Fraction of Ahmad's money left
= 1 - ⁵₇
= ²₇

Ahmad and Xuan had the same amount of money in the end. Make the numerators the same. LCM of 5 and 2 is 10.

⁵₆ of Xuan's money = ²₇ of Ahmad's money
¹⁰₁₂ of Xuan's money = ¹⁰₃₅ of Ahmad's money

Amount that Xuan had at first = 12 u
Amount that Ahmad had at first = 35 u

Amount that Xuan had less than Ahmad had at first
= 35 u - 12 u
= 23 u

23 u = 1334

1 u = 1334 ÷ 23 = 58

Amount that Ahmad had at first
= 35 u
= 35 x 58
= $2030

Answer(s): $2030