Tommy 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 brother and bought another 7 new buttons. In the end, Tommy had 27 buttons.

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

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

²₅ of his remaining buttons = 27 - 7 = 20
¹₅ of his remaining buttons = 20 ÷ 2 = 10
³₅ of his remaining buttons = 3 x 10 = 30

Number of buttons that Tommy gave to his brother = 30

(b)
⁵₅ of his remaining buttons = 5 x 10 = 50

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

¹₃ of his total buttons = 50 - 4 = 46
³₃ of his total buttons = 3 x 46 = 138

Number of buttons that Tommy had at first = 138 

Answer(s): (a) 30; (b) 138