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

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

(a)
Fraction of  his remaining buttons after he gave to his brother
= 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 Luis gave to his brother = 35

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

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

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

Number of buttons that Luis had at first = 156 

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