Simon had some buttons. He gave ²₃ of his buttons to Daniel and bought 4 new buttons. After that, he gave ⁵₈ of his remaining buttons to his sister and bought another 7 new buttons. In the end, Simon had 28 buttons.

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

(a)
Fraction of  his remaining buttons after he gave to his sister
= 1 - ⁵₈
= ³₈

³₈ of his remaining buttons = 28 - 7 = 21
¹₈ of his remaining buttons = 21 ÷ 3 = 7
⁵₈ of his remaining buttons = 5 x 7 = 35

Number of buttons that Simon gave to his sister = 35

(b)
⁸₈ of his remaining buttons = 8 x 7 = 56

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

¹₃ of his total buttons = 56 - 4 = 52
³₃ of his total buttons = 3 x 52 = 156

Number of buttons that Simon had at first = 156 

Answer(s): (a) 35; (b) 156