Tina, Xandra and Tammy had a total of 64 beads. The ratio of Xandra's beads to Tammy's beads was at first 4 : 9. After Tina and Xandra each gave half of their beads away, the 3 children had 41 beads left. How many beads did Tina and Xandra have at first?
| |
Tina |
Xandra |
Tammy |
Total |
| Before |
2 p |
4 u |
9 u |
64 |
| Change |
- 1 p |
- 2 u |
|
- 23 |
| After |
1 p |
2 u |
9 u |
41 |
Number of beads that Tina and Xandra gave away
= 64 - 41
= 23
1 p + 2 u = 23
1 p = 23 - 2 u --- (1)
1 p + 2 u + 9 u = 41
1 p + 11 u = 41
1 p = 41 - 11 u --- (2)
(1) = (2)
23 - 2 u = 41 - 11 u
11 u - 2 u = 41 - 23
9 u = 18
1 u = 18 ÷ 9 = 2
From (1)
1 p = 23 - 2 u
1 p = 23 - 2 x 2
1 p = 23 - 4 = 19
Number of beads that Tina and Xandra had at first
= 2 p + 4 u
= 2 x 19 + 4 x 2
= 38 + 18
= 56
Answer(s): 56
