Asher had some buttons. He gave ²₃ of his buttons to Vaidev 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, Asher had 42 buttons.

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

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

⁵₇ of his remaining buttons = 42 - 7 = 35
¹₇ of his remaining buttons = 35 ÷ 5 = 7
²₇ of his remaining buttons = 2 x 7 = 14

Number of buttons that Asher gave to his cousin = 14

(b)
⁷₇ of his remaining buttons = 7 x 7 = 49

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

¹₃ of his total buttons = 49 - 4 = 45
³₃ of his total buttons = 3 x 45 = 135

Number of buttons that Asher had at first = 135 

Answer(s): (a) 14; (b) 135