George and Min has some money each. If Min gives George $20, he will have 3 times as much money as her. If George gives Min $15, he will have the same amount of money as her. How much money does each person have respectively?
- George?
- Min?
| |
Case 1 |
Case 2 |
| |
George |
Min |
George |
Min |
| Before |
3 u - 20 |
1 u + 20 |
2 u + 15 |
2 u - 15 |
| Change |
+ 20 |
- 20 |
- 15 |
+ 15 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Min gives George some money or George gives Min some money, the total amount of money remains the same.
Total amount that George and Min have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that George and Min each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that George has at first in Case 1 and Case 2 is the same.
3 u - 20 = 2 u + 15
3 u - 2 u = 15 + 20
1 u = 35
Amount that George has
= 2 u + 15
= 2 x 35 + 15
= 70 + 15
= $85
(b)
Amount that Min has
= 1 u + 20
= 35 + 20
= $55
Answer(s): (a) $85; (b) $55
