Dana and Elyse have some money. If Dana spends $17, she will have
35 as much money as Elyse. If Elyse spends $12, Dana will have
78 as much money as Elyse. How much money does Elyse have?
| |
Case 1 |
Case 2 |
| |
Dana |
Elyse |
Dana |
Elyse |
| Before |
3 u + $17 |
5 u |
7 p |
8 p + $12 |
| Change |
- $17 |
|
|
- $12 |
| After |
3 u |
5 u |
7 p |
8 p |
The amount that Dana has at first in Case 1 and Case 2 is the same.
3 u + 17 = 7 p
3 u = 7 p - 17 --- (1)
The amount that Elyse has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 12 --- (2)
Make u the same.
(1)
x 515 u = 35 p - 85 --- (3)
(2)
x 315 u = 24 p + 36 --- (4)
(3) = (4)
35 p - 85 = 24 p + 36
35 p - 24 p = 85 + 36
11 p = 121
1 p = 121 ÷ 11 = 11
Amount that Elyse has
= 8 p + 12
= 8 x 11 + 12
= 88 + 12
= $100
Answer(s): $100
