The ratio of Jean's money to Penelope's money was 1 : 2. After Jean spent four times as much as Penelope, Jean and Penelope had $9 and $46 left respectively. Find the amount of money each of the girls have at first.
- Jean
- Penelope
| |
Make u the same
(1)x2 = (3) |
Jean
(1) |
Penelope
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 8 p |
- 4 p |
- 1 p |
| After |
18 |
9 |
46 |
(a)
1 u - 4 p = 9
2 u = 9 + 4 p --- (1)
2 u - 1 p = 46
2 u = 46 + 1 p --- (2)
(1)
x2
2 u = 18 + 8 p --- (3)
(3) = (2)
18 + 8 p = 46 + 1 p
8 p - 1 p = 46 - 18
7 p = 28
1 p = 28 ÷ 7 = 4
Amount that Jean had at first
= 9 + 4 p
= 9 + 4 x 4
= 9 + 16
= $25
(b)
Amount that Penelope had at first
= 18 + 8 p
= 18 + 8 x 4
= 18 + 32
= $50
Answer(s): (a) $25; (b) $50
