Eric had some buttons. He gave ³₄ of his buttons to Paul and bought 4 new buttons. After that, he gave ⁴₉ of his remaining buttons to his cousin and bought another 7 new buttons. In the end, Eric had 27 buttons.

1. How many buttons did Eric give to his cousin?
2. How many buttons did Eric have at first?

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

⁵₉ of his remaining buttons = 27 - 7 = 20
¹₉ of his remaining buttons = 20 ÷ 5 = 4
⁴₉ of his remaining buttons = 4 x 4 = 16

Number of buttons that Eric gave to his cousin = 16

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

Fraction of his total buttons after he gave to Paul
= 1 - ³₄
= ¹₄

¹₄ of his total buttons = 36 - 4 = 32
⁴₄ of his total buttons = 4 x 32 = 128

Number of buttons that Eric had at first = 128 

Answer(s): (a) 16; (b) 128