Owen and Yoko has some money each. If Yoko gives Owen $17, he will have 7 times as much money as her. If Owen gives Yoko $10, he will have the same amount of money as her. How much money does each person have respectively?
- Owen?
- Yoko?
| |
Case 1 |
Case 2 |
| |
Owen |
Yoko |
Owen |
Yoko |
| Before |
7 u - 17 |
1 u + 17 |
4 u + 10 |
4 u - 10 |
| Change |
+ 17 |
- 17 |
- 10 |
+ 10 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Yoko gives Owen some money or Owen gives Yoko some money, the total amount of money remains the same.
Total amount that Owen and Yoko have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Owen and Yoko each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Owen has at first in Case 1 and Case 2 is the same.
7 u - 17 = 4 u + 10
7 u - 4 u = 10 + 17
1 u = 27
Amount that Owen has
= 4 u + 10
= 4 x 27 + 10
= 108 + 10
= $118
(b)
Amount that Yoko has
= 1 u + 17
= 27 + 17
= $44
Answer(s): (a) $118; (b) $44
