Esther and Gabby have some money. If Esther spends $3, she will have
35 as much money as Gabby. If Gabby spends $9, Esther will have
56 as much money as Gabby. How much money does Gabby have?
| |
Case 1 |
Case 2 |
| |
Esther |
Gabby |
Esther |
Gabby |
| Before |
3 u + $3 |
5 u |
5 p |
6 p + $9 |
| Change |
- $3 |
|
|
- $9 |
| After |
3 u |
5 u |
5 p |
6 p |
The amount that Esther has at first in Case 1 and Case 2 is the same.
3 u + 3 = 5 p
3 u = 5 p - 3 --- (1)
The amount that Gabby has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 9 --- (2)
Make u the same.
(1)
x 515 u = 25 p - 15 --- (3)
(2)
x 315 u = 18 p + 27 --- (4)
(3) = (4)
25 p - 15 = 18 p + 27
25 p - 18 p = 15 + 27
7 p = 42
1 p = 42 ÷ 7 = 6
Amount that Gabby has
= 6 p + 9
= 6 x 6 + 9
= 36 + 9
= $45
Answer(s): $45
