Ivan and Diana has some money each. If Diana gives Ivan $13, he will have 3 times as much money as her. If Ivan gives Diana $20, he will have the same amount of money as her. How much money does each person have respectively?
- Ivan?
- Diana?
| |
Case 1 |
Case 2 |
| |
Ivan |
Diana |
Ivan |
Diana |
| Before |
3 u - 13 |
1 u + 13 |
2 u + 20 |
2 u - 20 |
| Change |
+ 13 |
- 13 |
- 20 |
+ 20 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Diana gives Ivan some money or Ivan gives Diana some money, the total amount of money remains the same.
Total amount that Ivan and Diana have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Ivan and Diana each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Ivan has at first in Case 1 and Case 2 is the same.
3 u - 13 = 2 u + 20
3 u - 2 u = 20 + 13
1 u = 33
Amount that Ivan has
= 2 u + 20
= 2 x 33 + 20
= 66 + 20
= $86
(b)
Amount that Diana has
= 1 u + 13
= 33 + 13
= $46
Answer(s): (a) $86; (b) $46
