Abi had $1564 less than Neave. Abi spent ¹₆ of her money and Neave spent ⁴₇ of his money. In the end, Neave and Abi had the same amount of money left. Find the amount of money Neave had at first.

	Abi	Neave	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 Abi's money left
= 1 - ¹₆
= ⁵₆

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

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

⁵₆ of Abi's money = ³₇ of Neave's money
¹⁵₁₈ of Abi's money = ¹⁵₃₅ of Neave's money

Amount that Abi had at first = 18 u
Amount that Neave had at first = 35 u

Amount that Abi had less than Neave had at first
= 35 u - 18 u
= 17 u

17 u = 1564

1 u = 1564 ÷ 17 = 92

Amount that Neave had at first
= 35 u
= 35 x 92
= $3220

Answer(s): $3220