Ethan and Jaslyn has some money each. If Jaslyn gives Ethan $15, he will have 7 times as much money as her. If Ethan gives Jaslyn $12, he will have the same amount of money as her. How much money does each person have respectively?
- Ethan?
- Jaslyn?
|
Case 1 |
Case 2 |
|
Ethan |
Jaslyn |
Ethan |
Jaslyn |
Before |
7 u - 15 |
1 u + 15 |
4 u + 12 |
4 u - 12 |
Change |
+ 15 |
- 15 |
- 12 |
+ 12 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Jaslyn gives Ethan some money or Ethan gives Jaslyn some money, the total amount of money remains the same.
Total amount that Ethan and Jaslyn have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Ethan and Jaslyn each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Ethan has at first in Case 1 and Case 2 is the same.
7 u - 15 = 4 u + 12
7 u - 4 u = 12 + 15
1 u = 27
Amount that Ethan has
= 4 u + 12
= 4 x 27 + 12
= 108 + 12
= $120
(b)
Amount that Jaslyn has
= 1 u + 15
= 27 + 15
= $42
Answer(s): (a) $120; (b) $42