Eva and Mary have some money. If Eva spends $15, she will have
35 as much money as Mary. If Mary spends $10, Eva will have
56 as much money as Mary. How much money does Eva have?
| |
Case 1 |
Case 2 |
| |
Eva |
Mary |
Eva |
Mary |
| Before |
3 u + $15 |
5 u |
5 p |
6 p + $10 |
| Change |
- $15 |
|
|
- $10 |
| After |
3 u |
5 u |
5 p |
6 p |
The amount that Eva has at first in Case 1 and Case 2 is the same.
3 u + 15 = 5 p
3 u = 5 p - 15 --- (1)
The amount that Mary has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 10 --- (2)
Make u the same.
(1)
x 515 u = 25 p - 75 --- (3)
(2)
x 315 u = 18 p + 30 --- (4)
(3) = (4)
25 p - 75 = 18 p + 30
25 p - 18 p = 75 + 30
7 p = 105
1 p = 105 ÷ 7 = 15
Amount that Eva has
= 5 p
= 5 x 15
= $75
Answer(s): $75
