Harry had some buttons. He gave ²₃ of his buttons to Bobby and bought 4 new buttons. After that, he gave ³₅ of his remaining buttons to his sister and bought another 7 new buttons. In the end, Harry had 33 buttons.

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

(a)
Fraction of  his remaining buttons after he gave to his sister
= 1 - ³₅
= ²₅

²₅ of his remaining buttons = 33 - 7 = 26
¹₅ of his remaining buttons = 26 ÷ 2 = 13
³₅ of his remaining buttons = 3 x 13 = 39

Number of buttons that Harry gave to his sister = 39

(b)
⁵₅ of his remaining buttons = 5 x 13 = 65

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

¹₃ of his total buttons = 65 - 4 = 61
³₃ of his total buttons = 3 x 61 = 183

Number of buttons that Harry had at first = 183 

Answer(s): (a) 39; (b) 183