Adam, Bryan and Charlie have $803.
After Adam spends ²₃ of his money,
Bryan spends ³₇ of his money and
Charlie spends ¹₄ of his money,
they have equal amount of money left.
Find the total amount that the 3 children spend.

	Adam	Bryan	Charlie
Before	3 x 12 = 36 u	7 x 3 = 21 u	4 x 4 = 16 u
Change	- 2 x 12 = - 24 u	- 3 x 3 = - 9 u	- 1 x 4 = - 4 u
After	1 x 12 =  12 u	4 x 3 = 12 u	3 x 4 = 12 u

The lowest common multiple of 1, 4 and 3 is 12.

Fraction of the amount left after Adam spends his money
= 1 - ²₃
= ¹₃

Fraction of the amount left after Bryan spends his money
= 1 - ³₇
= ⁴₇

Fraction of the amount left after Charlie spends his money
= 1 - ¹₄
= ³₄

Make the numerators the same.
1 x 123 x 12 of Adam's amount = 4 x 37 x 3 of Bryan's amount = 3 x 44 x 4 of Charlie's amount
1236 of Adam's amount = 1221 of Bryan's amount = 1216 of Charlie's amount

Total amount that they have at first
= 36 u + 21 u + 16 u
= 73 u

73 u = 803

1 u = 803 ÷ 73 = 11

Amount that Adam spends
= 36 u - 12 u
= 24 u

Amount that Bryan spends
= 21 u - 12 u
= 9 u

Amount that Charlie spends
= 16 u - 12 u
= 4 u

Amount that they spend
= 24 u + 9 u + 4 u
= 37 u
= 37 x 11
= $407

Answer(s): $407