Gem and Eva have some money. If Gem spends $38, she will have
25 as much money as Eva. If Eva spends $1, Gem will have
67 as much money as Eva. How much money does Gem have?
| |
Case 1 |
Case 2 |
| |
Gem |
Eva |
Gem |
Eva |
| Before |
2 u + $38 |
5 u |
6 p |
7 p + $1 |
| Change |
- $38 |
|
|
- $1 |
| After |
2 u |
5 u |
6 p |
7 p |
The amount that Gem has at first in Case 1 and Case 2 is the same.
2 u + 38 = 6 p
2 u = 6 p - 38 --- (1)
The amount that Eva has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 1 --- (2)
Make u the same.
(1)
x 510 u = 30 p - 190 --- (3)
(2)
x 210 u = 14 p + 2 --- (4)
(3) = (4)
30 p - 190 = 14 p + 2
30 p - 14 p = 190 + 2
16 p = 192
1 p = 192 ÷ 16 = 12
Amount that Gem has
= 6 p
= 6 x 12
= $72
Answer(s): $72
