Linda and Mary have some money. If Linda spends $22, she will have
25 as much money as Mary. If Mary spends $10, Linda will have
56 as much money as Mary. How much money does Linda have?
| |
Case 1 |
Case 2 |
| |
Linda |
Mary |
Linda |
Mary |
| Before |
2 u + $22 |
5 u |
5 p |
6 p + $10 |
| Change |
- $22 |
|
|
- $10 |
| After |
2 u |
5 u |
5 p |
6 p |
The amount that Linda has at first in Case 1 and Case 2 is the same.
2 u + 22 = 5 p
2 u = 5 p - 22 --- (1)
The amount that Mary has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 10 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 110 --- (3)
(2)
x 210 u = 12 p + 20 --- (4)
(3) = (4)
25 p - 110 = 12 p + 20
25 p - 12 p = 110 + 20
13 p = 130
1 p = 130 ÷ 13 = 10
Amount that Linda has
= 5 p
= 5 x 10
= $50
Answer(s): $50
