Jane, Risa and Anna had a total of 153 marbles. The ratio of Risa's marbles to Anna's marbles was at first 10 : 7. After Jane and Risa each gave half of their marbles away, the 3 children had 101 marbles left. How many marbles did Jane and Anna have at first?
| |
Jane |
Risa |
Anna |
Total |
| Before |
2 p |
10 u |
7 u |
153 |
| Change |
- 1 p |
- 5 u |
|
- 52 |
| After |
1 p |
5 u |
7 u |
101 |
Number of marbles that Jane and Risa gave away
= 153 - 101
= 52
1 p + 5 u = 52
1 p = 52 - 5 u --- (1)
1 p + 5 u + 7 u = 101
1 p + 12 u = 101
1 p = 101 - 12 u --- (2)
(1) = (2)
52 - 5 u = 101 - 12 u
12 u - 5 u = 101 - 52
7 u = 49
1 u = 49 ÷ 7 = 7
From (1)
1 p = 52 - 5 u
1 p = 52 - 5 x 7
1 p = 52 - 35 = 17
Number of marbles that Jane and Anna had at first
= 2 p + 7 u
= 2 x 17 + 7 x 7
= 34 + 49
= 83
Answer(s): 83
