Marion and Elyse have some money. If Marion spends $23, she will have
35 as much money as Elyse. If Elyse spends $2, Marion will have
78 as much money as Elyse. How much money does Marion have?
| |
Case 1 |
Case 2 |
| |
Marion |
Elyse |
Marion |
Elyse |
| Before |
3 u + $23 |
5 u |
7 p |
8 p + $2 |
| Change |
- $23 |
|
|
- $2 |
| After |
3 u |
5 u |
7 p |
8 p |
The amount that Marion has at first in Case 1 and Case 2 is the same.
3 u + 23 = 7 p
3 u = 7 p - 23 --- (1)
The amount that Elyse has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 2 --- (2)
Make u the same.
(1)
x 515 u = 35 p - 115 --- (3)
(2)
x 315 u = 24 p + 6 --- (4)
(3) = (4)
35 p - 115 = 24 p + 6
35 p - 24 p = 115 + 6
11 p = 121
1 p = 121 ÷ 11 = 11
Amount that Marion has
= 7 p
= 7 x 11
= $77
Answer(s): $77
