Jenson and Diana has some money each. If Diana gives Jenson $10, he will have 7 times as much money as her. If Jenson gives Diana $20, he will have the same amount of money as her. How much money does each person have respectively?
- Jenson?
- Diana?
| |
Case 1 |
Case 2 |
| |
Jenson |
Diana |
Jenson |
Diana |
| Before |
7 u - 10 |
1 u + 10 |
4 u + 20 |
4 u - 20 |
| Change |
+ 10 |
- 10 |
- 20 |
+ 20 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Diana gives Jenson some money or Jenson gives Diana some money, the total amount of money remains the same.
Total amount that Jenson and Diana have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Jenson and Diana each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Jenson has at first in Case 1 and Case 2 is the same.
7 u - 10 = 4 u + 20
7 u - 4 u = 20 + 10
1 u = 30
Amount that Jenson has
= 4 u + 20
= 4 x 30 + 20
= 120 + 20
= $140
(b)
Amount that Diana has
= 1 u + 10
= 30 + 10
= $40
Answer(s): (a) $140; (b) $40
