Tina, Lucy and Linda had a total of 72 beads. The ratio of Lucy's beads to Linda's beads was at first 8 : 9. After Tina and Lucy each gave half of their beads away, the 3 children had 45 beads left. How many beads did Tina and Lucy have at first?
| |
Tina |
Lucy |
Linda |
Total |
| Before |
2 p |
8 u |
9 u |
72 |
| Change |
- 1 p |
- 4 u |
|
- 27 |
| After |
1 p |
4 u |
9 u |
45 |
Number of beads that Tina and Lucy gave away
= 72 - 45
= 27
1 p + 4 u = 27
1 p = 27 - 4 u --- (1)
1 p + 4 u + 9 u = 45
1 p + 13 u = 45
1 p = 45 - 13 u --- (2)
(1) = (2)
27 - 4 u = 45 - 13 u
13 u - 4 u = 45 - 27
9 u = 18
1 u = 18 ÷ 9 = 2
From (1)
1 p = 27 - 4 u
1 p = 27 - 4 x 2
1 p = 27 - 8 = 19
Number of beads that Tina and Lucy had at first
= 2 p + 8 u
= 2 x 19 + 8 x 2
= 38 + 18
= 56
Answer(s): 56
