Albert had some buttons. He gave ²₃ of his buttons to Glen and bought 4 new buttons. After that, he gave ⁴₉ of his remaining buttons to his cousin and bought another 7 new buttons. In the end, Albert had 32 buttons.

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

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

⁵₉ of his remaining buttons = 32 - 7 = 25
¹₉ of his remaining buttons = 25 ÷ 5 = 5
⁴₉ of his remaining buttons = 4 x 5 = 20

Number of buttons that Albert gave to his cousin = 20

(b)
⁹₉ of his remaining buttons = 9 x 5 = 45

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

¹₃ of his total buttons = 45 - 4 = 41
³₃ of his total buttons = 3 x 41 = 123

Number of buttons that Albert had at first = 123 

Answer(s): (a) 20; (b) 123