Harry and Reggie gave away the same number of buttons. Harry gave away ³₅ of his buttons while Reggie gave ⁵₉ of his buttons away. Given that Harry had 20 buttons less than Reggie at first, how many buttons did Harry have at first?

	Harry	Reggie
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 Harry and Reggie gave away is the same.  Make the number of buttons that Harry and Reggie gave away the same. LCM of 3 and 5 is 15.

Number of buttons that Harry had at first = 25 u
Number of buttons that Reggie had at first = 27 u

Number of buttons that Harry had less than Reggie at first
= 27 u - 25 u
= 2 u

2 u = 20

1 u = 20 ÷ 2 = 10

Number of buttons that Harry had at first
= 25 u
= 25 x 10
= 250

Answer(s): 250