Erika and Nicole have some money. If Erika spends $10, she will have
25 as much money as Nicole. If Nicole spends $15, Erika will have
67 as much money as Nicole. How much money does Erika have?
| |
Case 1 |
Case 2 |
| |
Erika |
Nicole |
Erika |
Nicole |
| Before |
2 u + $10 |
5 u |
6 p |
7 p + $15 |
| Change |
- $10 |
|
|
- $15 |
| After |
2 u |
5 u |
6 p |
7 p |
The amount that Erika has at first in Case 1 and Case 2 is the same.
2 u + 10 = 6 p
2 u = 6 p - 10 --- (1)
The amount that Nicole has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 15 --- (2)
Make u the same.
(1)
x 510 u = 30 p - 50 --- (3)
(2)
x 210 u = 14 p + 30 --- (4)
(3) = (4)
30 p - 50 = 14 p + 30
30 p - 14 p = 50 + 30
16 p = 80
1 p = 80 ÷ 16 = 5
Amount that Erika has
= 6 p
= 6 x 5
= $30
Answer(s): $30
