Sarah and Rachel have some money. If Sarah spends $8, she will have
25 as much money as Rachel. If Rachel spends $16, Sarah will have
58 as much money as Rachel. How much money does Sarah have?
| |
Case 1 |
Case 2 |
| |
Sarah |
Rachel |
Sarah |
Rachel |
| Before |
2 u + $8 |
5 u |
5 p |
8 p + $16 |
| Change |
- $8 |
|
|
- $16 |
| After |
2 u |
5 u |
5 p |
8 p |
The amount that Sarah has at first in Case 1 and Case 2 is the same.
2 u + 8 = 5 p
2 u = 5 p - 8 --- (1)
The amount that Rachel has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 16 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 40 --- (3)
(2)
x 210 u = 16 p + 32 --- (4)
(3) = (4)
25 p - 40 = 16 p + 32
25 p - 16 p = 40 + 32
9 p = 72
1 p = 72 ÷ 9 = 8
Amount that Sarah has
= 5 p
= 5 x 8
= $40
Answer(s): $40
