Elijah and Pierre gave away the same number of buttons. Elijah gave away ³₅ of his buttons while Pierre gave ⁵₉ of his buttons away. Given that Elijah had 24 buttons less than Pierre at first, how many buttons did Elijah have at first?

	Elijah	Pierre
Before	5x5 = 25 u	9x3 = 27 u
Change	- 3x5 = - 15 u	- 5x3 = - 15 u
After	2x5 = 10 u	4x3 = 12 u

The number of buttons that Elijah and Pierre gave away is the same.  Make the number of buttons that Elijah and Pierre gave away the same. LCM of 3 and 5 is 15.

Number of buttons that Elijah had at first = 25 u
Number of buttons that Pierre had at first = 27 u

Number of buttons that Elijah had less than Pierre at first
= 27 u - 25 u
= 2 u

2 u = 24

1 u = 24 ÷ 2 = 12

Number of buttons that Elijah had at first
= 25 u
= 25 x 12
= 300

Answer(s): 300