Jane had $468 less than Daniel. Jane spent ¹₄ of her money and Daniel spent ⁵₇ of his money. In the end, Daniel and Jane had the same amount of money left. Find the amount of money Daniel had at first.

	Jane	Daniel	Difference
Before	4x2 = 8 u	7x3 = 21 u	13 u
Change	- 1x2 = - 2 u	- 5x3 = - 15 u
After	3x2 = 6 u	2x3 = 6 u

Fraction of Jane's money left
= 1 - ¹₄
= ³₄

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

Daniel and Jane had the same amount of money in the end. Make the numerators the same. LCM of 3 and 2 is 6.

³₄ of Jane's money = ²₇ of Daniel's money
⁶₈ of Jane's money = ⁶₂₁ of Daniel's money

Amount that Jane had at first = 8 u
Amount that Daniel had at first = 21 u

Amount that Jane had less than Daniel had at first
= 21 u - 8 u
= 13 u

13 u = 468

1 u = 468 ÷ 13 = 36

Amount that Daniel had at first
= 21 u
= 21 x 36
= $756

Answer(s): $756