Sarah and Olivia have some money. If Sarah spends $4, she will have
25 as much money as Olivia. If Olivia spends $47, Sarah will have
78 as much money as Olivia. How much money does Sarah have?
| |
Case 1 |
Case 2 |
| |
Sarah |
Olivia |
Sarah |
Olivia |
| Before |
2 u + $4 |
5 u |
7 p |
8 p + $47 |
| Change |
- $4 |
|
|
- $47 |
| After |
2 u |
5 u |
7 p |
8 p |
The amount that Sarah has at first in Case 1 and Case 2 is the same.
2 u + 4 = 7 p
2 u = 7 p - 4 --- (1)
The amount that Olivia has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 47 --- (2)
Make u the same.
(1)
x 510 u = 35 p - 20 --- (3)
(2)
x 210 u = 16 p + 94 --- (4)
(3) = (4)
35 p - 20 = 16 p + 94
35 p - 16 p = 20 + 94
19 p = 114
1 p = 114 ÷ 19 = 6
Amount that Sarah has
= 7 p
= 7 x 6
= $42
Answer(s): $42
