Howard had some coins. He gave ³₄ of his coins to Luke and bought 4 new coins. After that, he gave ⁵₉ of his remaining coins to his cousin and bought another 7 new coins. In the end, Howard had 31 coins.

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

(a)
Fraction of  his remaining coins after he gave to his cousin
= 1 - ⁵₉
= ⁴₉

⁴₉ of his remaining coins = 31 - 7 = 24
¹₉ of his remaining coins = 24 ÷ 4 = 6
⁵₉ of his remaining coins = 5 x 6 = 30

Number of coins that Howard gave to his cousin = 30

(b)
⁹₉ of his remaining coins = 9 x 6 = 54

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

¹₄ of his total coins = 54 - 4 = 50
⁴₄ of his total coins = 4 x 50 = 200

Number of coins that Howard had at first = 200 

Answer(s): (a) 30; (b) 200