Lucy and Tiffany have some money. If Lucy spends $25, she will have
25 as much money as Tiffany. If Tiffany spends $22, Lucy will have
56 as much money as Tiffany. How much money does Tiffany have?
| |
Case 1 |
Case 2 |
| |
Lucy |
Tiffany |
Lucy |
Tiffany |
| Before |
2 u + $25 |
5 u |
5 p |
6 p + $22 |
| Change |
- $25 |
|
|
- $22 |
| After |
2 u |
5 u |
5 p |
6 p |
The amount that Lucy has at first in Case 1 and Case 2 is the same.
2 u + 25 = 5 p
2 u = 5 p - 25 --- (1)
The amount that Tiffany has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 22 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 125 --- (3)
(2)
x 210 u = 12 p + 44 --- (4)
(3) = (4)
25 p - 125 = 12 p + 44
25 p - 12 p = 125 + 44
13 p = 169
1 p = 169 ÷ 13 = 13
Amount that Tiffany has
= 6 p + 22
= 6 x 13 + 22
= 78 + 22
= $100
Answer(s): $100
