Zane had some coins. He gave ³₄ of his coins to Carl and bought 4 new coins. After that, he gave ²₅ of his remaining coins to his sister and bought another 7 new coins. In the end, Zane had 37 coins.

1. How many coins did Zane give to his sister?
2. How many coins did Zane have at first?

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

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

Number of coins that Zane gave to his sister = 20

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

Fraction of his total coins after he gave to Carl
= 1 - ³₄
= ¹₄

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

Number of coins that Zane had at first = 184 

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