Gem and Gabby have some money. If Gem spends $14, she will have
35 as much money as Gabby. If Gabby spends $7, Gem will have
56 as much money as Gabby. How much money does Gem have?
| |
Case 1 |
Case 2 |
| |
Gem |
Gabby |
Gem |
Gabby |
| Before |
3 u + $14 |
5 u |
5 p |
6 p + $7 |
| Change |
- $14 |
|
|
- $7 |
| After |
3 u |
5 u |
5 p |
6 p |
The amount that Gem has at first in Case 1 and Case 2 is the same.
3 u + 14 = 5 p
3 u = 5 p - 14 --- (1)
The amount that Gabby has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 7 --- (2)
Make u the same.
(1)
x 515 u = 25 p - 70 --- (3)
(2)
x 315 u = 18 p + 21 --- (4)
(3) = (4)
25 p - 70 = 18 p + 21
25 p - 18 p = 70 + 21
7 p = 91
1 p = 91 ÷ 7 = 13
Amount that Gem has
= 5 p
= 5 x 13
= $65
Answer(s): $65
