Zeph had some marbles. He gave ²₃ of his marbles to Valen and bought 4 new marbles. After that, he gave ⁵₈ of his remaining marbles to his brother and bought another 7 new marbles. In the end, Zeph had 28 marbles.

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

(a)
Fraction of  his remaining marbles after he gave to his brother
= 1 - ⁵₈
= ³₈

³₈ of his remaining marbles = 28 - 7 = 21
¹₈ of his remaining marbles = 21 ÷ 3 = 7
⁵₈ of his remaining marbles = 5 x 7 = 35

Number of marbles that Zeph gave to his brother = 35

(b)
⁸₈ of his remaining marbles = 8 x 7 = 56

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

¹₃ of his total marbles = 56 - 4 = 52
³₃ of his total marbles = 3 x 52 = 156

Number of marbles that Zeph had at first = 156 

Answer(s): (a) 35; (b) 156