Raeann and Pamela have some money. If Raeann spends $20, she will have
25 as much money as Pamela. If Pamela spends $22, Raeann will have
67 as much money as Pamela. How much money does Raeann have?
| |
Case 1 |
Case 2 |
| |
Raeann |
Pamela |
Raeann |
Pamela |
| Before |
2 u + $20 |
5 u |
6 p |
7 p + $22 |
| Change |
- $20 |
|
|
- $22 |
| After |
2 u |
5 u |
6 p |
7 p |
The amount that Raeann has at first in Case 1 and Case 2 is the same.
2 u + 20 = 6 p
2 u = 6 p - 20 --- (1)
The amount that Pamela has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 22 --- (2)
Make u the same.
(1)
x 510 u = 30 p - 100 --- (3)
(2)
x 210 u = 14 p + 44 --- (4)
(3) = (4)
30 p - 100 = 14 p + 44
30 p - 14 p = 100 + 44
16 p = 144
1 p = 144 ÷ 16 = 9
Amount that Raeann has
= 6 p
= 6 x 9
= $54
Answer(s): $54
