The ratio of Joelle's money to Elyse's money was 1 : 3. After Joelle spent thrice as much as Elyse, Joelle and Elyse had $8 and $48 left respectively. Find the amount of money each of the girls have at first.
- Joelle
- Elyse
| |
Make u the same
(1)x3 = (3) |
Joelle
(1) |
Elyse
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 9 p |
- 3 p |
- 1 p |
| After |
24 |
8 |
48 |
(a)
1 u - 3 p = 8
3 u = 8 + 3 p --- (1)
3 u - 1 p = 48
3 u = 48 + 1 p --- (2)
(1)
x3
3 u = 24 + 9 p --- (3)
(3) = (2)
24 + 9 p = 48 + 1 p
9 p - 1 p = 48 - 24
8 p = 24
1 p = 24 ÷ 8 = 3
Amount that Joelle had at first
= 8 + 3 p
= 8 + 3 x 3
= 8 + 9
= $17
(b)
Amount that Elyse had at first
= 24 + 9 p
= 24 + 9 x 3
= 24 + 27
= $51
Answer(s): (a) $17; (b) $51
