Esther and Erika have some money. If Esther spends $6, she will have
25 as much money as Erika. If Erika spends $12, Esther will have
58 as much money as Erika. How much money does Esther have?
| |
Case 1 |
Case 2 |
| |
Esther |
Erika |
Esther |
Erika |
| Before |
2 u + $6 |
5 u |
5 p |
8 p + $12 |
| Change |
- $6 |
|
|
- $12 |
| After |
2 u |
5 u |
5 p |
8 p |
The amount that Esther has at first in Case 1 and Case 2 is the same.
2 u + 6 = 5 p
2 u = 5 p - 6 --- (1)
The amount that Erika has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 12 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 30 --- (3)
(2)
x 210 u = 16 p + 24 --- (4)
(3) = (4)
25 p - 30 = 16 p + 24
25 p - 16 p = 30 + 24
9 p = 54
1 p = 54 ÷ 9 = 6
Amount that Esther has
= 5 p
= 5 x 6
= $30
Answer(s): $30
