Xuan, Emily and Nicole had a total of 62 marbles. The ratio of Emily's marbles to Nicole's marbles was at first 8 : 3. After Xuan and Emily each gave half of their marbles away, the 3 children had 34 marbles left. How many marbles did Xuan and Emily have at first?
| |
Xuan |
Emily |
Nicole |
Total |
| Before |
2 p |
8 u |
3 u |
62 |
| Change |
- 1 p |
- 4 u |
|
- 28 |
| After |
1 p |
4 u |
3 u |
34 |
Number of marbles that Xuan and Emily gave away
= 62 - 34
= 28
1 p + 4 u = 28
1 p = 28 - 4 u --- (1)
1 p + 4 u + 3 u = 34
1 p + 7 u = 34
1 p = 34 - 7 u --- (2)
(1) = (2)
28 - 4 u = 34 - 7 u
7 u - 4 u = 34 - 28
3 u = 6
1 u = 6 ÷ 3 = 2
From (1)
1 p = 28 - 4 u
1 p = 28 - 4 x 2
1 p = 28 - 8 = 20
Number of marbles that Xuan and Emily had at first
= 2 p + 8 u
= 2 x 20 + 8 x 2
= 40 + 6
= 46
Answer(s): 46
