The ratio of Dana's money to Jaslyn's money was 1 : 2. After Dana spent four times as much as Jaslyn, Dana and Jaslyn had $9 and $53 left respectively. Find the amount of money each of the girls have at first.
- Dana
- Jaslyn
| |
Make u the same
(1)x2 = (3) |
Dana
(1) |
Jaslyn
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 8 p |
- 4 p |
- 1 p |
| After |
18 |
9 |
53 |
(a)
1 u - 4 p = 9
2 u = 9 + 4 p --- (1)
2 u - 1 p = 53
2 u = 53 + 1 p --- (2)
(1)
x2
2 u = 18 + 8 p --- (3)
(3) = (2)
18 + 8 p = 53 + 1 p
8 p - 1 p = 53 - 18
7 p = 35
1 p = 35 ÷ 7 = 5
Amount that Dana had at first
= 9 + 4 p
= 9 + 4 x 5
= 9 + 20
= $29
(b)
Amount that Jaslyn had at first
= 18 + 8 p
= 18 + 8 x 5
= 18 + 40
= $58
Answer(s): (a) $29; (b) $58
