Eric had some coins. He gave ²₃ of his coins to Valen and bought 4 new coins. After that, he gave ⁴₉ of his remaining coins to his brother and bought another 7 new coins. In the end, Eric had 42 coins.

1. How many coins did Eric give to his brother?
2. How many coins did Eric have at first?

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

⁵₉ of his remaining coins = 42 - 7 = 35
¹₉ of his remaining coins = 35 ÷ 5 = 7
⁴₉ of his remaining coins = 4 x 7 = 28

Number of coins that Eric gave to his brother = 28

(b)
⁹₉ of his remaining coins = 9 x 7 = 63

Fraction of his total coins after he gave to Valen
= 1 - ²₃
= ¹₃

¹₃ of his total coins = 63 - 4 = 59
³₃ of his total coins = 3 x 59 = 177

Number of coins that Eric had at first = 177 

Answer(s): (a) 28; (b) 177