Mark and Fiona has some money each. If Fiona gives Mark $20, he will have 5 times as much money as her. If Mark gives Fiona $10, he will have the same amount of money as her. How much money does each person have respectively?
- Mark?
- Fiona?
| |
Case 1 |
Case 2 |
| |
Mark |
Fiona |
Mark |
Fiona |
| Before |
5 u - 20 |
1 u + 20 |
3 u + 10 |
3 u - 10 |
| Change |
+ 20 |
- 20 |
- 10 |
+ 10 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Fiona gives Mark some money or Mark gives Fiona some money, the total amount of money remains the same.
Total amount that Mark and Fiona have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Mark and Fiona each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Mark has at first in Case 1 and Case 2 is the same.
5 u - 20 = 3 u + 10
5 u - 3 u = 10 + 20
1 u = 30
Amount that Mark has
= 3 u + 10
= 3 x 30 + 10
= 90 + 10
= $100
(b)
Amount that Fiona has
= 1 u + 20
= 30 + 20
= $50
Answer(s): (a) $100; (b) $50
