Tommy, Perry and Vincent had a total of 141 beads. The ratio of the number of beads that Perry had to the number of beads that Vincent had was 6 : 7. After Tommy and Perry each gave away half of their beads, the 3 children had 102 beads left. How many beads did Perry and Vincent have in the end?
| |
Tommy |
Perry |
Vincent |
Total |
| Before |
2 p |
6 u |
7 u |
141 |
| Change |
- 1 p |
- 3 u |
|
- 39 |
| After |
1 p |
3 u |
7 u |
102 |
Total number of beads that Tommy and Perry gave away
= 141 - 102
= 39
1 p + 3 u = 39 --- (1)
1 p + 3 u + 7 u = 102
1 p + 10 u = 102 --- (2)
(2) - (1)
(1 p + 10 u) - (1 p + 3 u) = 102 - 39
10 u - 3 u = 63
7 u = 63
1 u = 63 ÷ 7 = 9
Total number of beads that Perry and Vincent had in the end
= 3 u + 7 u
= 10 u
= 10 x 9
= 90
Answer(s): 90
