Esther and Sabrina have some money. If Esther spends $2, she will have
45 as much money as Sabrina. If Sabrina spends $1, Esther will have
67 as much money as Sabrina. How much money does Sabrina have?
| |
Case 1 |
Case 2 |
| |
Esther |
Sabrina |
Esther |
Sabrina |
| Before |
4 u + $2 |
5 u |
6 p |
7 p + $1 |
| Change |
- $2 |
|
|
- $1 |
| After |
4 u |
5 u |
6 p |
7 p |
The amount that Esther has at first in Case 1 and Case 2 is the same.
4 u + 2 = 6 p
4 u = 6 p - 2 --- (1)
The amount that Sabrina has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 1 --- (2)
Make u the same.
(1)
x 520 u = 30 p - 10 --- (3)
(2)
x 420 u = 28 p + 4 --- (4)
(3) = (4)
30 p - 10 = 28 p + 4
30 p - 28 p = 10 + 4
2 p = 14
1 p = 14 ÷ 2 = 7
Amount that Sabrina has
= 7 p + 1
= 7 x 7 + 1
= 49 + 1
= $50
Answer(s): $50
