George had some buttons. He gave ²₃ of his buttons to Albert and bought 4 new buttons. After that, he gave ²₇ of his remaining buttons to his sister and bought another 7 new buttons. In the end, George had 37 buttons.

1. How many buttons did George give to his sister?
2. How many buttons did George have at first?

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

⁵₇ of his remaining buttons = 37 - 7 = 30
¹₇ of his remaining buttons = 30 ÷ 5 = 6
²₇ of his remaining buttons = 2 x 6 = 12

Number of buttons that George gave to his sister = 12

(b)
⁷₇ of his remaining buttons = 7 x 6 = 42

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

¹₃ of his total buttons = 42 - 4 = 38
³₃ of his total buttons = 3 x 38 = 114

Number of buttons that George had at first = 114 

Answer(s): (a) 12; (b) 114