Tommy, Sam and Oliver had a total of 94 beads. The ratio of the number of beads that Sam had to the number of beads that Oliver had was 8 : 7. After Tommy and Sam each gave away half of their beads, the 3 children had 68 beads left. How many beads did Sam and Oliver have at first?
| |
Tommy |
Sam |
Oliver |
Total |
| Before |
2 p |
8 u |
7 u |
94 |
| Change |
- 1 p |
- 4 u |
|
- 26 |
| After |
1 p |
4 u |
7 u |
68 |
Total number of beads that Tommy and Sam gave away
= 94 - 68
= 26
1 p + 4 u = 26 --- (1)
1 p + 4 u + 7 u = 68
1 p + 11 u = 68 --- (2)
(2) - (1)
(1 p + 11 u) - (1 p + 4 u) = 68 - 26
11 u - 4 u = 42
7 u = 42
1 u = 42 ÷ 7 = 6
Total number of beads that Sam and Oliver had at first
= 8 u + 7 u
= 15 u
= 15 x 6
= 90
Answer(s): 90
