The ratio of Jane's money to Natalie's money was 1 : 2. After Jane spent four times as much as Natalie, Jane and Natalie had $8 and $44 left respectively. Find the amount of money each of the girls have at first.
- Jane
- Natalie
| |
Make u the same
(1)x2 = (3) |
Jane
(1) |
Natalie
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 8 p |
- 4 p |
- 1 p |
| After |
16 |
8 |
44 |
(a)
1 u - 4 p = 8
2 u = 8 + 4 p --- (1)
2 u - 1 p = 44
2 u = 44 + 1 p --- (2)
(1)
x2
2 u = 16 + 8 p --- (3)
(3) = (2)
16 + 8 p = 44 + 1 p
8 p - 1 p = 44 - 16
7 p = 28
1 p = 28 ÷ 7 = 4
Amount that Jane had at first
= 8 + 4 p
= 8 + 4 x 4
= 8 + 16
= $24
(b)
Amount that Natalie had at first
= 16 + 8 p
= 16 + 8 x 4
= 16 + 32
= $48
Answer(s): (a) $24; (b) $48
