Gabby and Hazel have some money. If Gabby spends $1, she will have
45 as much money as Hazel. If Hazel spends $7, Gabby will have
78 as much money as Hazel. How much money does Gabby have?
| |
Case 1 |
Case 2 |
| |
Gabby |
Hazel |
Gabby |
Hazel |
| Before |
4 u + $1 |
5 u |
7 p |
8 p + $7 |
| Change |
- $1 |
|
|
- $7 |
| After |
4 u |
5 u |
7 p |
8 p |
The amount that Gabby has at first in Case 1 and Case 2 is the same.
4 u + 1 = 7 p
4 u = 7 p - 1 --- (1)
The amount that Hazel has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 7 --- (2)
Make u the same.
(1)
x 520 u = 35 p - 5 --- (3)
(2)
x 420 u = 32 p + 28 --- (4)
(3) = (4)
35 p - 5 = 32 p + 28
35 p - 32 p = 5 + 28
3 p = 33
1 p = 33 ÷ 3 = 11
Amount that Gabby has
= 7 p
= 7 x 11
= $77
Answer(s): $77
