The ratio of Zara's money to Elyse's money was 1 : 3. After Zara spent thrice as much as Elyse, Zara and Elyse had $6 and $50 left respectively. Find the amount of money each of the girls have at first.
- Zara
- Elyse
| |
Make u the same
(1)x3 = (3) |
Zara
(1) |
Elyse
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 9 p |
- 3 p |
- 1 p |
| After |
18 |
6 |
50 |
(a)
1 u - 3 p = 6
3 u = 6 + 3 p --- (1)
3 u - 1 p = 50
3 u = 50 + 1 p --- (2)
(1)
x3
3 u = 18 + 9 p --- (3)
(3) = (2)
18 + 9 p = 50 + 1 p
9 p - 1 p = 50 - 18
8 p = 32
1 p = 32 ÷ 8 = 4
Amount that Zara had at first
= 6 + 3 p
= 6 + 3 x 4
= 6 + 12
= $18
(b)
Amount that Elyse had at first
= 18 + 9 p
= 18 + 9 x 4
= 18 + 36
= $54
Answer(s): (a) $18; (b) $54
