Raeann, Olivia and Jade had a total of 193 beads. The ratio of Olivia's beads to Jade's beads was at first 8 : 7. After Raeann and Olivia each gave half of their beads away, the 3 children had 135 beads left. How many beads did Raeann and Jade have at first?
| |
Raeann |
Olivia |
Jade |
Total |
| Before |
2 p |
8 u |
7 u |
193 |
| Change |
- 1 p |
- 4 u |
|
- 58 |
| After |
1 p |
4 u |
7 u |
135 |
Number of beads that Raeann and Olivia gave away
= 193 - 135
= 58
1 p + 4 u = 58
1 p = 58 - 4 u --- (1)
1 p + 4 u + 7 u = 135
1 p + 11 u = 135
1 p = 135 - 11 u --- (2)
(1) = (2)
58 - 4 u = 135 - 11 u
11 u - 4 u = 135 - 58
7 u = 77
1 u = 77 ÷ 7 = 11
From (1)
1 p = 58 - 4 u
1 p = 58 - 4 x 11
1 p = 58 - 44 = 14
Number of beads that Raeann and Jade had at first
= 2 p + 7 u
= 2 x 14 + 7 x 11
= 28 + 77
= 105
Answer(s): 105
