Riordan and Kathy has some money each. If Kathy gives Riordan $20, he will have 7 times as much money as her. If Riordan gives Kathy $17, he will have the same amount of money as her. How much money does each person have respectively?
- Riordan?
- Kathy?
| |
Case 1 |
Case 2 |
| |
Riordan |
Kathy |
Riordan |
Kathy |
| Before |
7 u - 20 |
1 u + 20 |
4 u + 17 |
4 u - 17 |
| Change |
+ 20 |
- 20 |
- 17 |
+ 17 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Kathy gives Riordan some money or Riordan gives Kathy some money, the total amount of money remains the same.
Total amount that Riordan and Kathy have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Riordan and Kathy each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Riordan has at first in Case 1 and Case 2 is the same.
7 u - 20 = 4 u + 17
7 u - 4 u = 17 + 20
1 u = 37
Amount that Riordan has
= 4 u + 17
= 4 x 37 + 17
= 148 + 17
= $165
(b)
Amount that Kathy has
= 1 u + 20
= 37 + 20
= $57
Answer(s): (a) $165; (b) $57
