Japheth and Liam gave away the same number of buttons. Japheth gave away ³₄ of his buttons while Liam gave ⁴₉ of his buttons away. Given that Japheth had 11 buttons less than Liam at first, how many buttons did Japheth have at first?

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

The number of buttons that Japheth and Liam gave away is the same.  Make the number of buttons that Japheth and Liam gave away the same. LCM of 3 and 4 is 12.

Number of buttons that Japheth had at first = 16 u
Number of buttons that Liam had at first = 27 u

Number of buttons that Japheth had less than Liam at first
= 27 u - 16 u
= 11 u

11 u = 11

1 u = 11 ÷ 11 = 1

Number of buttons that Japheth had at first
= 16 u
= 16 x 1
= 16

Answer(s): 16