Carl had some marbles. He gave ²₃ of his marbles to Oscar 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, Carl had 43 marbles.

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

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

³₅ of his remaining marbles = 43 - 7 = 36
¹₅ of his remaining marbles = 36 ÷ 3 = 12
²₅ of his remaining marbles = 2 x 12 = 24

Number of marbles that Carl gave to his cousin = 24

(b)
⁵₅ of his remaining marbles = 5 x 12 = 60

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

¹₃ of his total marbles = 60 - 4 = 56
³₃ of his total marbles = 3 x 56 = 168

Number of marbles that Carl had at first = 168 

Answer(s): (a) 24; (b) 168