The ratio of Olivia's money to Shannon's money was 1 : 2. After Olivia spent thrice as much as Shannon, Olivia and Shannon had $8 and $41 left respectively. Find the amount of money each of the girls have at first.
- Olivia
- Shannon
| |
Make u the same
(1)x2 = (3) |
Olivia
(1) |
Shannon
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
16 |
8 |
41 |
(a)
1 u - 3 p = 8
2 u = 8 + 3 p --- (1)
2 u - 1 p = 41
2 u = 41 + 1 p --- (2)
(1)
x2
2 u = 16 + 6 p --- (3)
(3) = (2)
16 + 6 p = 41 + 1 p
6 p - 1 p = 41 - 16
5 p = 25
1 p = 25 ÷ 5 = 5
Amount that Olivia had at first
= 8 + 3 p
= 8 + 3 x 5
= 8 + 15
= $23
(b)
Amount that Shannon had at first
= 16 + 6 p
= 16 + 6 x 5
= 16 + 30
= $46
Answer(s): (a) $23; (b) $46
