Kathy and Esther have some money. If Kathy spends $3, she will have
35 as much money as Esther. If Esther spends $3, Kathy will have
57 as much money as Esther. How much money does Esther have?
| |
Case 1 |
Case 2 |
| |
Kathy |
Esther |
Kathy |
Esther |
| Before |
3 u + $3 |
5 u |
5 p |
7 p + $3 |
| Change |
- $3 |
|
|
- $3 |
| After |
3 u |
5 u |
5 p |
7 p |
The amount that Kathy has at first in Case 1 and Case 2 is the same.
3 u + 3 = 5 p
3 u = 5 p - 3 --- (1)
The amount that Esther has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 3 --- (2)
Make u the same.
(1)
x 515 u = 25 p - 15 --- (3)
(2)
x 315 u = 21 p + 9 --- (4)
(3) = (4)
25 p - 15 = 21 p + 9
25 p - 21 p = 15 + 9
4 p = 24
1 p = 24 ÷ 4 = 6
Amount that Esther has
= 7 p + 3
= 7 x 6 + 3
= 42 + 3
= $45
Answer(s): $45
