Nick had some buttons. He gave ³₄ of his buttons to Ken and bought 4 new buttons. After that, he gave ³₈ of his remaining buttons to his cousin and bought another 7 new buttons. In the end, Nick had 32 buttons.

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

(a)
Fraction of  his remaining buttons after he gave to his cousin
= 1 - ³₈
= ⁵₈

⁵₈ of his remaining buttons = 32 - 7 = 25
¹₈ of his remaining buttons = 25 ÷ 5 = 5
³₈ of his remaining buttons = 3 x 5 = 15

Number of buttons that Nick gave to his cousin = 15

(b)
⁸₈ of his remaining buttons = 8 x 5 = 40

Fraction of his total buttons after he gave to Ken
= 1 - ³₄
= ¹₄

¹₄ of his total buttons = 40 - 4 = 36
⁴₄ of his total buttons = 4 x 36 = 144

Number of buttons that Nick had at first = 144 

Answer(s): (a) 15; (b) 144