Flynn had some buttons. He gave ³₄ of his buttons to Albert and bought 4 new buttons. After that, he gave ³₈ of his remaining buttons to his sister and bought another 7 new buttons. In the end, Flynn had 27 buttons.

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

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

⁵₈ of his remaining buttons = 27 - 7 = 20
¹₈ of his remaining buttons = 20 ÷ 5 = 4
³₈ of his remaining buttons = 3 x 4 = 12

Number of buttons that Flynn gave to his sister = 12

(b)
⁸₈ of his remaining buttons = 8 x 4 = 32

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

¹₄ of his total buttons = 32 - 4 = 28
⁴₄ of his total buttons = 4 x 28 = 112

Number of buttons that Flynn had at first = 112 

Answer(s): (a) 12; (b) 112