Oscar had some marbles. He gave ⁶₇ of his marbles to Perry and bought 4 new marbles. After that, he gave ²₇ of his remaining marbles to his sister and bought another 7 new marbles. In the end, Oscar had 22 marbles.

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

(a)
Fraction of  his remaining marbles after he gave to his sister
= 1 - ²₇
= ⁵₇

⁵₇ of his remaining marbles = 22 - 7 = 15
¹₇ of his remaining marbles = 15 ÷ 5 = 3
²₇ of his remaining marbles = 2 x 3 = 6

Number of marbles that Oscar gave to his sister = 6

(b)
⁷₇ of his remaining marbles = 7 x 3 = 21

Fraction of his total marbles after he gave to Perry
= 1 - ⁶₇
= ¹₇

¹₇ of his total marbles = 21 - 4 = 17
⁷₇ of his total marbles = 7 x 17 = 119

Number of marbles that Oscar had at first = 119 

Answer(s): (a) 6; (b) 119