Jaslyn and Gem have some money. If Jaslyn spends $3, she will have
25 as much money as Gem. If Gem spends $40, Jaslyn will have
78 as much money as Gem. How much money does Gem have?
| |
Case 1 |
Case 2 |
| |
Jaslyn |
Gem |
Jaslyn |
Gem |
| Before |
2 u + $3 |
5 u |
7 p |
8 p + $40 |
| Change |
- $3 |
|
|
- $40 |
| After |
2 u |
5 u |
7 p |
8 p |
The amount that Jaslyn has at first in Case 1 and Case 2 is the same.
2 u + 3 = 7 p
2 u = 7 p - 3 --- (1)
The amount that Gem has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 40 --- (2)
Make u the same.
(1)
x 510 u = 35 p - 15 --- (3)
(2)
x 210 u = 16 p + 80 --- (4)
(3) = (4)
35 p - 15 = 16 p + 80
35 p - 16 p = 15 + 80
19 p = 95
1 p = 95 ÷ 19 = 5
Amount that Gem has
= 8 p + 40
= 8 x 5 + 40
= 40 + 40
= $80
Answer(s): $80
