Eva and Hazel have some money. If Eva spends $12, she will have
25 as much money as Hazel. If Hazel spends $15, Eva will have
58 as much money as Hazel. How much money does Eva have?
| |
Case 1 |
Case 2 |
| |
Eva |
Hazel |
Eva |
Hazel |
| Before |
2 u + $12 |
5 u |
5 p |
8 p + $15 |
| Change |
- $12 |
|
|
- $15 |
| After |
2 u |
5 u |
5 p |
8 p |
The amount that Eva has at first in Case 1 and Case 2 is the same.
2 u + 12 = 5 p
2 u = 5 p - 12 --- (1)
The amount that Hazel has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 15 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 60 --- (3)
(2)
x 210 u = 16 p + 30 --- (4)
(3) = (4)
25 p - 60 = 16 p + 30
25 p - 16 p = 60 + 30
9 p = 90
1 p = 90 ÷ 9 = 10
Amount that Eva has
= 5 p
= 5 x 10
= $50
Answer(s): $50
