Vincent had some coins. He gave ²₃ of his coins to Daniel and bought 4 new coins. After that, he gave ³₅ of his remaining coins to his brother and bought another 7 new coins. In the end, Vincent had 21 coins.

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

(a)
Fraction of  his remaining coins after he gave to his brother
= 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 Vincent gave to his brother = 21

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

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

¹₃ of his total coins = 35 - 4 = 31
³₃ of his total coins = 3 x 31 = 93

Number of coins that Vincent had at first = 93 

Answer(s): (a) 21; (b) 93