Gabby and Hilda have some money. If Gabby spends $30, she will have
25 as much money as Hilda. If Hilda spends $20, Gabby will have
78 as much money as Hilda. How much money does Gabby have?
| |
Case 1 |
Case 2 |
| |
Gabby |
Hilda |
Gabby |
Hilda |
| Before |
2 u + $30 |
5 u |
7 p |
8 p + $20 |
| Change |
- $30 |
|
|
- $20 |
| After |
2 u |
5 u |
7 p |
8 p |
The amount that Gabby has at first in Case 1 and Case 2 is the same.
2 u + 30 = 7 p
2 u = 7 p - 30 --- (1)
The amount that Hilda has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 20 --- (2)
Make u the same.
(1)
x 510 u = 35 p - 150 --- (3)
(2)
x 210 u = 16 p + 40 --- (4)
(3) = (4)
35 p - 150 = 16 p + 40
35 p - 16 p = 150 + 40
19 p = 190
1 p = 190 ÷ 19 = 10
Amount that Gabby has
= 7 p
= 7 x 10
= $70
Answer(s): $70
