Xandra and Cindy have some money. If Xandra spends $4, she will have
25 as much money as Cindy. If Cindy spends $8, Xandra will have
58 as much money as Cindy. How much money does Cindy have?
| |
Case 1 |
Case 2 |
| |
Xandra |
Cindy |
Xandra |
Cindy |
| Before |
2 u + $4 |
5 u |
5 p |
8 p + $8 |
| Change |
- $4 |
|
|
- $8 |
| After |
2 u |
5 u |
5 p |
8 p |
The amount that Xandra has at first in Case 1 and Case 2 is the same.
2 u + 4 = 5 p
2 u = 5 p - 4 --- (1)
The amount that Cindy has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 8 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 20 --- (3)
(2)
x 210 u = 16 p + 16 --- (4)
(3) = (4)
25 p - 20 = 16 p + 16
25 p - 16 p = 20 + 16
9 p = 36
1 p = 36 ÷ 9 = 4
Amount that Cindy has
= 8 p + 8
= 8 x 4 + 8
= 32 + 8
= $40
Answer(s): $40
