Jen and Vanessa have some money. If Jen spends $12, she will have
25 as much money as Vanessa. If Vanessa spends $27, Jen will have
78 as much money as Vanessa. How much money does Jen have?
| |
Case 1 |
Case 2 |
| |
Jen |
Vanessa |
Jen |
Vanessa |
| Before |
2 u + $12 |
5 u |
7 p |
8 p + $27 |
| Change |
- $12 |
|
|
- $27 |
| After |
2 u |
5 u |
7 p |
8 p |
The amount that Jen has at first in Case 1 and Case 2 is the same.
2 u + 12 = 7 p
2 u = 7 p - 12 --- (1)
The amount that Vanessa has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 27 --- (2)
Make u the same.
(1)
x 510 u = 35 p - 60 --- (3)
(2)
x 210 u = 16 p + 54 --- (4)
(3) = (4)
35 p - 60 = 16 p + 54
35 p - 16 p = 60 + 54
19 p = 114
1 p = 114 ÷ 19 = 6
Amount that Jen has
= 7 p
= 7 x 6
= $42
Answer(s): $42
