Vaidev, Asher and Billy had a total of 78 beads. The ratio of the number of beads that Asher had to the number of beads that Billy had was 2 : 3. After Vaidev and Asher each gave away half of their beads, the 3 children had 57 beads left. How many beads did Asher and Billy have at first?
| |
Vaidev |
Asher |
Billy |
Total |
| Before |
2 p |
2 u |
3 u |
78 |
| Change |
- 1 p |
- 1 u |
|
- 21 |
| After |
1 p |
1 u |
3 u |
57 |
Total number of beads that Vaidev and Asher gave away
= 78 - 57
= 21
1 p + 1 u = 21 --- (1)
1 p + 1 u + 3 u = 57
1 p + 4 u = 57 --- (2)
(2) - (1)
(1 p + 4 u) - (1 p + 1 u) = 57 - 21
4 u - 1 u = 36
3 u = 36
1 u = 36 ÷ 3 = 12
Total number of beads that Asher and Billy had at first
= 2 u + 3 u
= 5 u
= 5 x 12
= 60
Answer(s): 60
