The ratio of Risa's money to Shannon's money was 1 : 3. After Risa spent five times as much as Shannon, Risa and Shannon had $9 and $55 left respectively. Find the amount of money each of the girls have at first.
- Risa
- Shannon
| |
Make u the same
(1)x3 = (3) |
Risa
(1) |
Shannon
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 15 p |
- 5 p |
- 1 p |
| After |
27 |
9 |
55 |
(a)
1 u - 5 p = 9
3 u = 9 + 5 p --- (1)
3 u - 1 p = 55
3 u = 55 + 1 p --- (2)
(1)
x3
3 u = 27 + 15 p --- (3)
(3) = (2)
27 + 15 p = 55 + 1 p
15 p - 1 p = 55 - 27
14 p = 28
1 p = 28 ÷ 14 = 2
Amount that Risa had at first
= 9 + 5 p
= 9 + 5 x 2
= 9 + 10
= $19
(b)
Amount that Shannon had at first
= 27 + 15 p
= 27 + 15 x 2
= 27 + 30
= $57
Answer(s): (a) $19; (b) $57
