Sean, Billy and Glen had a total of 140 beads. The ratio of the number of beads that Billy had to the number of beads that Glen had was 2 : 9. After Sean and Billy each gave away half of their beads, the 3 children had 124 beads left. How many beads did Billy and Glen have in the end?
| |
Sean |
Billy |
Glen |
Total |
| Before |
2 p |
2 u |
9 u |
140 |
| Change |
- 1 p |
- 1 u |
|
- 16 |
| After |
1 p |
1 u |
9 u |
124 |
Total number of beads that Sean and Billy gave away
= 140 - 124
= 16
1 p + 1 u = 16 --- (1)
1 p + 1 u + 9 u = 124
1 p + 10 u = 124 --- (2)
(2) - (1)
(1 p + 10 u) - (1 p + 1 u) = 124 - 16
10 u - 1 u = 108
9 u = 108
1 u = 108 ÷ 9 = 12
Total number of beads that Billy and Glen had in the end
= 1 u + 9 u
= 10 u
= 10 x 12
= 120
Answer(s): 120
