Julie and Marion have some money. If Julie spends $8, she will have
35 as much money as Marion. If Marion spends $5, Julie will have
78 as much money as Marion. How much money does Julie have?
| |
Case 1 |
Case 2 |
| |
Julie |
Marion |
Julie |
Marion |
| Before |
3 u + $8 |
5 u |
7 p |
8 p + $5 |
| Change |
- $8 |
|
|
- $5 |
| After |
3 u |
5 u |
7 p |
8 p |
The amount that Julie has at first in Case 1 and Case 2 is the same.
3 u + 8 = 7 p
3 u = 7 p - 8 --- (1)
The amount that Marion has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 5 --- (2)
Make u the same.
(1)
x 515 u = 35 p - 40 --- (3)
(2)
x 315 u = 24 p + 15 --- (4)
(3) = (4)
35 p - 40 = 24 p + 15
35 p - 24 p = 40 + 15
11 p = 55
1 p = 55 ÷ 11 = 5
Amount that Julie has
= 7 p
= 7 x 5
= $35
Answer(s): $35
