Gem and Cathy have some money. If Gem spends $17, she will have
25 as much money as Cathy. If Cathy spends $3, Gem will have
56 as much money as Cathy. How much money does Gem have?
| |
Case 1 |
Case 2 |
| |
Gem |
Cathy |
Gem |
Cathy |
| Before |
2 u + $17 |
5 u |
5 p |
6 p + $3 |
| Change |
- $17 |
|
|
- $3 |
| After |
2 u |
5 u |
5 p |
6 p |
The amount that Gem has at first in Case 1 and Case 2 is the same.
2 u + 17 = 5 p
2 u = 5 p - 17 --- (1)
The amount that Cathy has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 3 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 85 --- (3)
(2)
x 210 u = 12 p + 6 --- (4)
(3) = (4)
25 p - 85 = 12 p + 6
25 p - 12 p = 85 + 6
13 p = 91
1 p = 91 ÷ 13 = 7
Amount that Gem has
= 5 p
= 5 x 7
= $35
Answer(s): $35
