Rael had some buttons. He gave ³₄ of his buttons to Glen and bought 4 new buttons. After that, he gave ²₅ of his remaining buttons to his cousin and bought another 7 new buttons. In the end, Rael had 37 buttons.

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

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

³₅ of his remaining buttons = 37 - 7 = 30
¹₅ of his remaining buttons = 30 ÷ 3 = 10
²₅ of his remaining buttons = 2 x 10 = 20

Number of buttons that Rael gave to his cousin = 20

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

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

¹₄ of his total buttons = 50 - 4 = 46
⁴₄ of his total buttons = 4 x 46 = 184

Number of buttons that Rael had at first = 184 

Answer(s): (a) 20; (b) 184