Luke had some marbles. He gave ³₄ of his marbles to Caden and bought 4 new marbles. After that, he gave ³₅ of his remaining marbles to his cousin and bought another 7 new marbles. In the end, Luke had 27 marbles.

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

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

²₅ of his remaining marbles = 27 - 7 = 20
¹₅ of his remaining marbles = 20 ÷ 2 = 10
³₅ of his remaining marbles = 3 x 10 = 30

Number of marbles that Luke gave to his cousin = 30

(b)
⁵₅ of his remaining marbles = 5 x 10 = 50

Fraction of his total marbles after he gave to Caden
= 1 - ³₄
= ¹₄

¹₄ of his total marbles = 50 - 4 = 46
⁴₄ of his total marbles = 4 x 46 = 184

Number of marbles that Luke had at first = 184 

Answer(s): (a) 30; (b) 184