Carl, Archie and Bobby had a total of 62 beads. The ratio of the number of beads that Archie had to the number of beads that Bobby had was 6 : 7. After Carl and Archie each gave away half of their beads, the 3 children had 45 beads left. How many beads did Archie and Bobby have in the end?
| |
Carl |
Archie |
Bobby |
Total |
| Before |
2 p |
6 u |
7 u |
62 |
| Change |
- 1 p |
- 3 u |
|
- 17 |
| After |
1 p |
3 u |
7 u |
45 |
Total number of beads that Carl and Archie gave away
= 62 - 45
= 17
1 p + 3 u = 17 --- (1)
1 p + 3 u + 7 u = 45
1 p + 10 u = 45 --- (2)
(2) - (1)
(1 p + 10 u) - (1 p + 3 u) = 45 - 17
10 u - 3 u = 28
7 u = 28
1 u = 28 ÷ 7 = 4
Total number of beads that Archie and Bobby had in the end
= 3 u + 7 u
= 10 u
= 10 x 4
= 40
Answer(s): 40
