Eva and Gillian have some money. If Eva spends $5, she will have
25 as much money as Gillian. If Gillian spends $4, Eva will have
57 as much money as Gillian. How much money does Gillian have?
| |
Case 1 |
Case 2 |
| |
Eva |
Gillian |
Eva |
Gillian |
| Before |
2 u + $5 |
5 u |
5 p |
7 p + $4 |
| Change |
- $5 |
|
|
- $4 |
| After |
2 u |
5 u |
5 p |
7 p |
The amount that Eva has at first in Case 1 and Case 2 is the same.
2 u + 5 = 5 p
2 u = 5 p - 5 --- (1)
The amount that Gillian has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 4 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 25 --- (3)
(2)
x 210 u = 14 p + 8 --- (4)
(3) = (4)
25 p - 25 = 14 p + 8
25 p - 14 p = 25 + 8
11 p = 33
1 p = 33 ÷ 11 = 3
Amount that Gillian has
= 7 p + 4
= 7 x 3 + 4
= 21 + 4
= $25
Answer(s): $25
