Gem and Joelle have some money. If Gem spends $18, she will have
25 as much money as Joelle. If Joelle spends $10, Gem will have
57 as much money as Joelle. How much money does Joelle have?
| |
Case 1 |
Case 2 |
| |
Gem |
Joelle |
Gem |
Joelle |
| Before |
2 u + $18 |
5 u |
5 p |
7 p + $10 |
| Change |
- $18 |
|
|
- $10 |
| After |
2 u |
5 u |
5 p |
7 p |
The amount that Gem has at first in Case 1 and Case 2 is the same.
2 u + 18 = 5 p
2 u = 5 p - 18 --- (1)
The amount that Joelle has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 10 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 90 --- (3)
(2)
x 210 u = 14 p + 20 --- (4)
(3) = (4)
25 p - 90 = 14 p + 20
25 p - 14 p = 90 + 20
11 p = 110
1 p = 110 ÷ 11 = 10
Amount that Joelle has
= 7 p + 10
= 7 x 10 + 10
= 70 + 10
= $80
Answer(s): $80
