Emily and Ivory have some money. If Emily spends $17, she will have
25 as much money as Ivory. If Ivory spends $18, Emily will have
57 as much money as Ivory. How much money does Emily have?
| |
Case 1 |
Case 2 |
| |
Emily |
Ivory |
Emily |
Ivory |
| Before |
2 u + $17 |
5 u |
5 p |
7 p + $18 |
| Change |
- $17 |
|
|
- $18 |
| After |
2 u |
5 u |
5 p |
7 p |
The amount that Emily has at first in Case 1 and Case 2 is the same.
2 u + 17 = 5 p
2 u = 5 p - 17 --- (1)
The amount that Ivory has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 18 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 85 --- (3)
(2)
x 210 u = 14 p + 36 --- (4)
(3) = (4)
25 p - 85 = 14 p + 36
25 p - 14 p = 85 + 36
11 p = 121
1 p = 121 ÷ 11 = 11
Amount that Emily has
= 5 p
= 5 x 11
= $55
Answer(s): $55
