Tom had some marbles. He gave ⁷₈ of his marbles to Xavier and bought 4 new marbles. After that, he gave ³₈ of his remaining marbles to his brother and bought another 7 new marbles. In the end, Tom had 22 marbles.

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

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

⁵₈ of his remaining marbles = 22 - 7 = 15
¹₈ of his remaining marbles = 15 ÷ 5 = 3
³₈ of his remaining marbles = 3 x 3 = 9

Number of marbles that Tom gave to his brother = 9

(b)
⁸₈ of his remaining marbles = 8 x 3 = 24

Fraction of his total marbles after he gave to Xavier
= 1 - ⁷₈
= ¹₈

¹₈ of his total marbles = 24 - 4 = 20
⁸₈ of his total marbles = 8 x 20 = 160

Number of marbles that Tom had at first = 160 

Answer(s): (a) 9; (b) 160