Billy had some buttons. He gave ²₃ of his buttons to Glen and bought 4 new buttons. After that, he gave ²₇ of his remaining buttons to his cousin and bought another 7 new buttons. In the end, Billy had 47 buttons.

1. How many buttons did Billy give to his cousin?
2. How many buttons did Billy have at first?

(a)
Fraction of  his remaining buttons after he gave to his cousin
= 1 - ²₇
= ⁵₇

⁵₇ of his remaining buttons = 47 - 7 = 40
¹₇ of his remaining buttons = 40 ÷ 5 = 8
²₇ of his remaining buttons = 2 x 8 = 16

Number of buttons that Billy gave to his cousin = 16

(b)
⁷₇ of his remaining buttons = 7 x 8 = 56

Fraction of his total buttons after he gave to Glen
= 1 - ²₃
= ¹₃

¹₃ of his total buttons = 56 - 4 = 52
³₃ of his total buttons = 3 x 52 = 156

Number of buttons that Billy had at first = 156 

Answer(s): (a) 16; (b) 156