Zara, Xuan and Betty had a total of 88 beads. The ratio of Xuan's beads to Betty's beads was at first 4 : 7. After Zara and Xuan each gave half of their beads away, the 3 children had 58 beads left. How many beads did Zara and Xuan have at first?
| |
Zara |
Xuan |
Betty |
Total |
| Before |
2 p |
4 u |
7 u |
88 |
| Change |
- 1 p |
- 2 u |
|
- 30 |
| After |
1 p |
2 u |
7 u |
58 |
Number of beads that Zara and Xuan gave away
= 88 - 58
= 30
1 p + 2 u = 30
1 p = 30 - 2 u --- (1)
1 p + 2 u + 7 u = 58
1 p + 9 u = 58
1 p = 58 - 9 u --- (2)
(1) = (2)
30 - 2 u = 58 - 9 u
9 u - 2 u = 58 - 30
7 u = 28
1 u = 28 ÷ 7 = 4
From (1)
1 p = 30 - 2 u
1 p = 30 - 2 x 4
1 p = 30 - 8 = 22
Number of beads that Zara and Xuan had at first
= 2 p + 4 u
= 2 x 22 + 4 x 4
= 44 + 28
= 72
Answer(s): 72
