Peter had some coins. He gave ²₃ of his coins to Luis and bought 4 new coins. After that, he gave ²₅ of his remaining coins to his brother and bought another 7 new coins. In the end, Peter had 34 coins.

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

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

³₅ of his remaining coins = 34 - 7 = 27
¹₅ of his remaining coins = 27 ÷ 3 = 9
²₅ of his remaining coins = 2 x 9 = 18

Number of coins that Peter gave to his brother = 18

(b)
⁵₅ of his remaining coins = 5 x 9 = 45

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

¹₃ of his total coins = 45 - 4 = 41
³₃ of his total coins = 3 x 41 = 123

Number of coins that Peter had at first = 123 

Answer(s): (a) 18; (b) 123