Ahmad, Charlie and George had a total of 76 beads. The ratio of the number of beads that Charlie had to the number of beads that George had was 4 : 5. After Ahmad and Charlie each gave away half of their beads, the 3 children had 53 beads left. How many beads did Charlie and George have at first?
| |
Ahmad |
Charlie |
George |
Total |
| Before |
2 p |
4 u |
5 u |
76 |
| Change |
- 1 p |
- 2 u |
|
- 23 |
| After |
1 p |
2 u |
5 u |
53 |
Total number of beads that Ahmad and Charlie gave away
= 76 - 53
= 23
1 p + 2 u = 23 --- (1)
1 p + 2 u + 5 u = 53
1 p + 7 u = 53 --- (2)
(2) - (1)
(1 p + 7 u) - (1 p + 2 u) = 53 - 23
7 u - 2 u = 30
5 u = 30
1 u = 30 ÷ 5 = 6
Total number of beads that Charlie and George had at first
= 4 u + 5 u
= 9 u
= 9 x 6
= 54
Answer(s): 54
