Ivan had some coins. He gave ³₄ of his coins to Paul and bought 4 new coins. After that, he gave ³₅ of his remaining coins to his sister and bought another 7 new coins. In the end, Ivan had 21 coins.

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

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

²₅ of his remaining coins = 21 - 7 = 14
¹₅ of his remaining coins = 14 ÷ 2 = 7
³₅ of his remaining coins = 3 x 7 = 21

Number of coins that Ivan gave to his sister = 21

(b)
⁵₅ of his remaining coins = 5 x 7 = 35

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

¹₄ of his total coins = 35 - 4 = 31
⁴₄ of his total coins = 4 x 31 = 124

Number of coins that Ivan had at first = 124 

Answer(s): (a) 21; (b) 124