Vincent had some marbles. He gave ²₃ of his marbles to Riordan and bought 4 new marbles. After that, he gave ²₅ of his remaining marbles to his cousin and bought another 7 new marbles. In the end, Vincent had 28 marbles.

1. How many marbles did Vincent give to his cousin?
2. How many marbles did Vincent have at first?

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

³₅ of his remaining marbles = 28 - 7 = 21
¹₅ of his remaining marbles = 21 ÷ 3 = 7
²₅ of his remaining marbles = 2 x 7 = 14

Number of marbles that Vincent gave to his cousin = 14

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

Fraction of his total marbles after he gave to Riordan
= 1 - ²₃
= ¹₃

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

Number of marbles that Vincent had at first = 93 

Answer(s): (a) 14; (b) 93