Olivia, Dana and Gillian had a total of 150 beads. The ratio of Dana's beads to Gillian's beads was at first 8 : 7. After Olivia and Dana each gave half of their beads away, the 3 children had 103 beads left. How many beads did Olivia and Gillian have at first?
| |
Olivia |
Dana |
Gillian |
Total |
| Before |
2 p |
8 u |
7 u |
150 |
| Change |
- 1 p |
- 4 u |
|
- 47 |
| After |
1 p |
4 u |
7 u |
103 |
Number of beads that Olivia and Dana gave away
= 150 - 103
= 47
1 p + 4 u = 47
1 p = 47 - 4 u --- (1)
1 p + 4 u + 7 u = 103
1 p + 11 u = 103
1 p = 103 - 11 u --- (2)
(1) = (2)
47 - 4 u = 103 - 11 u
11 u - 4 u = 103 - 47
7 u = 56
1 u = 56 ÷ 7 = 8
From (1)
1 p = 47 - 4 u
1 p = 47 - 4 x 8
1 p = 47 - 32 = 15
Number of beads that Olivia and Gillian had at first
= 2 p + 7 u
= 2 x 15 + 7 x 8
= 30 + 56
= 86
Answer(s): 86
