Ahmad had some buttons. He gave ²₃ of his buttons to Oliver and bought 4 new buttons. After that, he gave ⁴₉ of his remaining buttons to his sister and bought another 7 new buttons. In the end, Ahmad had 22 buttons.

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

(a)
Fraction of  his remaining buttons after he gave to his sister
= 1 - ⁴₉
= ⁵₉

⁵₉ of his remaining buttons = 22 - 7 = 15
¹₉ of his remaining buttons = 15 ÷ 5 = 3
⁴₉ of his remaining buttons = 4 x 3 = 12

Number of buttons that Ahmad gave to his sister = 12

(b)
⁹₉ of his remaining buttons = 9 x 3 = 27

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

¹₃ of his total buttons = 27 - 4 = 23
³₃ of his total buttons = 3 x 23 = 69

Number of buttons that Ahmad had at first = 69 

Answer(s): (a) 12; (b) 69