Neave had some buttons. He gave ²₃ of his buttons to Jenson 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, Neave had 22 buttons.

1. How many buttons did Neave give to his brother?
2. How many buttons did Neave 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 Neave gave to his brother = 12

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

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

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

Number of buttons that Neave had at first = 69 

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