Ethan and Diana has some money each. If Diana gives Ethan $15, he will have 7 times as much money as her. If Ethan gives Diana $20, he will have the same amount of money as her. How much money does each person have respectively?
- Ethan?
- Diana?
|
Case 1 |
Case 2 |
|
Ethan |
Diana |
Ethan |
Diana |
Before |
7 u - 15 |
1 u + 15 |
4 u + 20 |
4 u - 20 |
Change |
+ 15 |
- 15 |
- 20 |
+ 20 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Diana gives Ethan some money or Ethan gives Diana some money, the total amount of money remains the same.
Total amount that Ethan and Diana have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Ethan and Diana 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 + 20
7 u - 4 u = 20 + 15
1 u = 35
Amount that Ethan has
= 4 u + 20
= 4 x 35 + 20
= 140 + 20
= $160
(b)
Amount that Diana has
= 1 u + 15
= 35 + 15
= $50
Answer(s): (a) $160; (b) $50