The ratio of Esther's money to Sabrina's money was 1 : 2. After Esther spent thrice as much as Sabrina, Esther and Sabrina had $6 and $47 left respectively. Find the amount of money each of the girls have at first.
- Esther
- Sabrina
| |
Make u the same
(1)x2 = (3) |
Esther
(1) |
Sabrina
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
12 |
6 |
47 |
(a)
1 u - 3 p = 6
2 u = 6 + 3 p --- (1)
2 u - 1 p = 47
2 u = 47 + 1 p --- (2)
(1)
x2
2 u = 12 + 6 p --- (3)
(3) = (2)
12 + 6 p = 47 + 1 p
6 p - 1 p = 47 - 12
5 p = 35
1 p = 35 ÷ 5 = 7
Amount that Esther had at first
= 6 + 3 p
= 6 + 3 x 7
= 6 + 21
= $27
(b)
Amount that Sabrina had at first
= 12 + 6 p
= 12 + 6 x 7
= 12 + 42
= $54
Answer(s): (a) $27; (b) $54
