Opal had $1853 less than Ken. Opal spent ¹₆ of her money and Ken spent ⁴₇ of his money. In the end, Ken and Opal had the same amount of money left. Find the amount of money Ken had at first.

	Opal	Ken	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 Opal's money left
= 1 - ¹₆
= ⁵₆

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

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

⁵₆ of Opal's money = ³₇ of Ken's money
¹⁵₁₈ of Opal's money = ¹⁵₃₅ of Ken's money

Amount that Opal had at first = 18 u
Amount that Ken had at first = 35 u

Amount that Opal had less than Ken had at first
= 35 u - 18 u
= 17 u

17 u = 1853

1 u = 1853 ÷ 17 = 109

Amount that Ken had at first
= 35 u
= 35 x 109
= $3815

Answer(s): $3815