Ken had some buttons. He gave ⁵₆ of his buttons to David and bought 4 new buttons. After that, he gave ⁵₉ of his remaining buttons to his sister and bought another 7 new buttons. In the end, Ken had 23 buttons.

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

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

⁴₉ of his remaining buttons = 23 - 7 = 16
¹₉ of his remaining buttons = 16 ÷ 4 = 4
⁵₉ of his remaining buttons = 5 x 4 = 20

Number of buttons that Ken gave to his sister = 20

(b)
⁹₉ of his remaining buttons = 9 x 4 = 36

Fraction of his total buttons after he gave to David
= 1 - ⁵₆
= ¹₆

¹₆ of his total buttons = 36 - 4 = 32
⁶₆ of his total buttons = 6 x 32 = 192

Number of buttons that Ken had at first = 192 

Answer(s): (a) 20; (b) 192