Gabby and Tiffany have some money. If Gabby spends $12, she will have
25 as much money as Tiffany. If Tiffany spends $34, Gabby will have
67 as much money as Tiffany. How much money does Tiffany have?
| |
Case 1 |
Case 2 |
| |
Gabby |
Tiffany |
Gabby |
Tiffany |
| Before |
2 u + $12 |
5 u |
6 p |
7 p + $34 |
| Change |
- $12 |
|
|
- $34 |
| After |
2 u |
5 u |
6 p |
7 p |
The amount that Gabby has at first in Case 1 and Case 2 is the same.
2 u + 12 = 6 p
2 u = 6 p - 12 --- (1)
The amount that Tiffany has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 34 --- (2)
Make u the same.
(1)
x 510 u = 30 p - 60 --- (3)
(2)
x 210 u = 14 p + 68 --- (4)
(3) = (4)
30 p - 60 = 14 p + 68
30 p - 14 p = 60 + 68
16 p = 128
1 p = 128 ÷ 16 = 8
Amount that Tiffany has
= 7 p + 34
= 7 x 8 + 34
= 56 + 34
= $90
Answer(s): $90
