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

1. How many buttons did Fred give to his brother?
2. How many buttons did Fred have at first?

(a)
Fraction of  his remaining buttons after he gave to his brother
= 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 Fred gave to his brother = 12

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

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

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

Number of buttons that Fred had at first = 69 

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