George and Yen has some money each. If Yen gives George $20, he will have 7 times as much money as her. If George gives Yen $13, he will have the same amount of money as her. How much money does each person have respectively?
- George?
- Yen?
| |
Case 1 |
Case 2 |
| |
George |
Yen |
George |
Yen |
| Before |
7 u - 20 |
1 u + 20 |
4 u + 13 |
4 u - 13 |
| Change |
+ 20 |
- 20 |
- 13 |
+ 13 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Yen gives George some money or George gives Yen some money, the total amount of money remains the same.
Total amount that George and Yen have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that George and Yen each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that George has at first in Case 1 and Case 2 is the same.
7 u - 20 = 4 u + 13
7 u - 4 u = 13 + 20
1 u = 33
Amount that George has
= 4 u + 13
= 4 x 33 + 13
= 132 + 13
= $145
(b)
Amount that Yen has
= 1 u + 20
= 33 + 20
= $53
Answer(s): (a) $145; (b) $53
