Oscar and Diana has some money each. If Diana gives Oscar $19, he will have 5 times as much money as her. If Oscar gives Diana $18, he will have the same amount of money as her. How much money does each person have respectively?
- Oscar?
- Diana?
| |
Case 1 |
Case 2 |
| |
Oscar |
Diana |
Oscar |
Diana |
| Before |
5 u - 19 |
1 u + 19 |
3 u + 18 |
3 u - 18 |
| Change |
+ 19 |
- 19 |
- 18 |
+ 18 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Diana gives Oscar some money or Oscar gives Diana some money, the total amount of money remains the same.
Total amount that Oscar and Diana have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Oscar and Diana each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Oscar has at first in Case 1 and Case 2 is the same.
5 u - 19 = 3 u + 18
5 u - 3 u = 18 + 19
1 u = 37
Amount that Oscar has
= 3 u + 18
= 3 x 37 + 18
= 111 + 18
= $129
(b)
Amount that Diana has
= 1 u + 19
= 37 + 19
= $56
Answer(s): (a) $129; (b) $56
