The ratio of Zara's money to Winnie's money was 1 : 3. After Zara spent thrice as much as Winnie, Zara and Winnie had $4 and $44 left respectively. Find the amount of money each of the girls have at first.
- Zara
- Winnie
| |
Make u the same
(1)x3 = (3) |
Zara
(1) |
Winnie
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 9 p |
- 3 p |
- 1 p |
| After |
12 |
4 |
44 |
(a)
1 u - 3 p = 4
3 u = 4 + 3 p --- (1)
3 u - 1 p = 44
3 u = 44 + 1 p --- (2)
(1)
x3
3 u = 12 + 9 p --- (3)
(3) = (2)
12 + 9 p = 44 + 1 p
9 p - 1 p = 44 - 12
8 p = 32
1 p = 32 ÷ 8 = 4
Amount that Zara had at first
= 4 + 3 p
= 4 + 3 x 4
= 4 + 12
= $16
(b)
Amount that Winnie had at first
= 12 + 9 p
= 12 + 9 x 4
= 12 + 36
= $48
Answer(s): (a) $16; (b) $48
