Dylan had some marbles. He gave ⁵₆ of his marbles to Riordan and bought 4 new marbles. After that, he gave ²₅ of his remaining marbles to his brother and bought another 7 new marbles. In the end, Dylan had 28 marbles.

1. How many marbles did Dylan give to his brother?
2. How many marbles did Dylan have at first?

(a)
Fraction of  his remaining marbles after he gave to his brother
= 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 Dylan gave to his brother = 14

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

Fraction of his total marbles after he gave to Riordan
= 1 - ⁵₆
= ¹₆

¹₆ of his total marbles = 35 - 4 = 31
⁶₆ of his total marbles = 6 x 31 = 186

Number of marbles that Dylan had at first = 186 

Answer(s): (a) 14; (b) 186