Bobby had some marbles. He gave ²₃ of his marbles to Jenson and bought 4 new marbles. After that, he gave ⁵₉ of his remaining marbles to his sister and bought another 7 new marbles. In the end, Bobby had 27 marbles.

1. How many marbles did Bobby give to his sister?
2. How many marbles did Bobby have at first?

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

⁴₉ of his remaining marbles = 27 - 7 = 20
¹₉ of his remaining marbles = 20 ÷ 4 = 5
⁵₉ of his remaining marbles = 5 x 5 = 25

Number of marbles that Bobby gave to his sister = 25

(b)
⁹₉ of his remaining marbles = 9 x 5 = 45

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

¹₃ of his total marbles = 45 - 4 = 41
³₃ of his total marbles = 3 x 41 = 123

Number of marbles that Bobby had at first = 123 

Answer(s): (a) 25; (b) 123