Jack had some coins. He gave ³₄ of his coins to Luke and bought 4 new coins. After that, he gave ³₈ of his remaining coins to his cousin and bought another 7 new coins. In the end, Jack had 37 coins.

1. How many coins did Jack give to his cousin?
2. How many coins did Jack have at first?

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

⁵₈ of his remaining coins = 37 - 7 = 30
¹₈ of his remaining coins = 30 ÷ 5 = 6
³₈ of his remaining coins = 3 x 6 = 18

Number of coins that Jack gave to his cousin = 18

(b)
⁸₈ of his remaining coins = 8 x 6 = 48

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

¹₄ of his total coins = 48 - 4 = 44
⁴₄ of his total coins = 4 x 44 = 176

Number of coins that Jack had at first = 176 

Answer(s): (a) 18; (b) 176