The ratio of Jade's money to Cathy's money was 1 : 3. After Jade spent four times as much as Cathy, Jade and Cathy had $6 and $40 left respectively. Find the amount of money each of the girls have at first.
- Jade
- Cathy
| |
Make u the same
(1)x3 = (3) |
Jade
(1) |
Cathy
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 12 p |
- 4 p |
- 1 p |
| After |
18 |
6 |
40 |
(a)
1 u - 4 p = 6
3 u = 6 + 4 p --- (1)
3 u - 1 p = 40
3 u = 40 + 1 p --- (2)
(1)
x3
3 u = 18 + 12 p --- (3)
(3) = (2)
18 + 12 p = 40 + 1 p
12 p - 1 p = 40 - 18
11 p = 22
1 p = 22 ÷ 11 = 2
Amount that Jade had at first
= 6 + 4 p
= 6 + 4 x 2
= 6 + 8
= $14
(b)
Amount that Cathy had at first
= 18 + 12 p
= 18 + 12 x 2
= 18 + 24
= $42
Answer(s): (a) $14; (b) $42
