Howard and Fiona has some money each. If Fiona gives Howard $10, he will have 5 times as much money as her. If Howard gives Fiona $11, he will have the same amount of money as her. How much money does each person have respectively?
- Howard?
- Fiona?
|
Case 1 |
Case 2 |
|
Howard |
Fiona |
Howard |
Fiona |
Before |
5 u - 10 |
1 u + 10 |
3 u + 11 |
3 u - 11 |
Change |
+ 10 |
- 10 |
- 11 |
+ 11 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Fiona gives Howard some money or Howard gives Fiona some money, the total amount of money remains the same.
Total amount that Howard and Fiona have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Howard and Fiona each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Howard has at first in Case 1 and Case 2 is the same.
5 u - 10 = 3 u + 11
5 u - 3 u = 11 + 10
1 u = 21
Amount that Howard has
= 3 u + 11
= 3 x 21 + 11
= 63 + 11
= $74
(b)
Amount that Fiona has
= 1 u + 10
= 21 + 10
= $31
Answer(s): (a) $74; (b) $31