Elijah and Billy gave away the same number of marbles. Elijah gave away ³₄ of his marbles while Billy gave ⁴₉ of his marbles away. Given that Elijah had 22 marbles less than Billy at first, how many marbles did Elijah have at first?

	Elijah	Billy
Before	4x4 = 16 u	9x3 = 27 u
Change	- 3x4 = - 12 u	- 4x3 = - 12 u
After	1x4 = 4 u	5x3 = 15 u

The number of marbles that Elijah and Billy gave away is the same.  Make the number of marbles that Elijah and Billy gave away the same. LCM of 3 and 4 is 12.

Number of marbles that Elijah had at first = 16 u
Number of marbles that Billy had at first = 27 u

Number of marbles that Elijah had less than Billy at first
= 27 u - 16 u
= 11 u

11 u = 22

1 u = 22 ÷ 11 = 2

Number of marbles that Elijah had at first
= 16 u
= 16 x 2
= 32

Answer(s): 32