Roshel, Cathy and Shannon had a total of 157 beads. The ratio of Cathy's beads to Shannon's beads was at first 8 : 3. After Roshel and Cathy each gave half of their beads away, the 3 children had 95 beads left. How many beads did Roshel and Shannon have at first?
| |
Roshel |
Cathy |
Shannon |
Total |
| Before |
2 p |
8 u |
3 u |
157 |
| Change |
- 1 p |
- 4 u |
|
- 62 |
| After |
1 p |
4 u |
3 u |
95 |
Number of beads that Roshel and Cathy gave away
= 157 - 95
= 62
1 p + 4 u = 62
1 p = 62 - 4 u --- (1)
1 p + 4 u + 3 u = 95
1 p + 7 u = 95
1 p = 95 - 7 u --- (2)
(1) = (2)
62 - 4 u = 95 - 7 u
7 u - 4 u = 95 - 62
3 u = 33
1 u = 33 ÷ 3 = 11
From (1)
1 p = 62 - 4 u
1 p = 62 - 4 x 11
1 p = 62 - 44 = 18
Number of beads that Roshel and Shannon had at first
= 2 p + 3 u
= 2 x 18 + 3 x 11
= 36 + 33
= 69
Answer(s): 69
