Henry had some buttons. He gave ⁶₇ of his buttons to Paul 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, Henry had 22 buttons.

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

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

⁵₇ of his remaining buttons = 22 - 7 = 15
¹₇ of his remaining buttons = 15 ÷ 5 = 3
²₇ of his remaining buttons = 2 x 3 = 6

Number of buttons that Henry gave to his cousin = 6

(b)
⁷₇ of his remaining buttons = 7 x 3 = 21

Fraction of his total buttons after he gave to Paul
= 1 - ⁶₇
= ¹₇

¹₇ of his total buttons = 21 - 4 = 17
⁷₇ of his total buttons = 7 x 17 = 119

Number of buttons that Henry had at first = 119 

Answer(s): (a) 6; (b) 119