Harry and Cathy has some money each. If Cathy gives Harry $13, he will have 5 times as much money as her. If Harry gives Cathy $12, he will have the same amount of money as her. How much money does each person have respectively?
- Harry?
- Cathy?
|
Case 1 |
Case 2 |
|
Harry |
Cathy |
Harry |
Cathy |
Before |
5 u - 13 |
1 u + 13 |
3 u + 12 |
3 u - 12 |
Change |
+ 13 |
- 13 |
- 12 |
+ 12 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Cathy gives Harry some money or Harry gives Cathy some money, the total amount of money remains the same.
Total amount that Harry and Cathy have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Harry and Cathy each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Harry has at first in Case 1 and Case 2 is the same.
5 u - 13 = 3 u + 12
5 u - 3 u = 12 + 13
1 u = 25
Amount that Harry has
= 3 u + 12
= 3 x 25 + 12
= 75 + 12
= $87
(b)
Amount that Cathy has
= 1 u + 13
= 25 + 13
= $38
Answer(s): (a) $87; (b) $38