Caden had some marbles. He gave ²₃ of his marbles to Jack and bought 4 new marbles. After that, he gave ⁴₉ of his remaining marbles to his brother and bought another 7 new marbles. In the end, Caden had 27 marbles.

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

(a)
Fraction of  his remaining marbles after he gave to his brother
= 1 - ⁴₉
= ⁵₉

⁵₉ of his remaining marbles = 27 - 7 = 20
¹₉ of his remaining marbles = 20 ÷ 5 = 4
⁴₉ of his remaining marbles = 4 x 4 = 16

Number of marbles that Caden gave to his brother = 16

(b)
⁹₉ of his remaining marbles = 9 x 4 = 36

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

¹₃ of his total marbles = 36 - 4 = 32
³₃ of his total marbles = 3 x 32 = 96

Number of marbles that Caden had at first = 96 

Answer(s): (a) 16; (b) 96