Ben and Min has some money each. If Min gives Ben $19, he will have 5 times as much money as her. If Ben gives Min $18, he will have the same amount of money as her. How much money does each person have respectively?
- Ben?
- Min?
|
Case 1 |
Case 2 |
|
Ben |
Min |
Ben |
Min |
Before |
5 u - 19 |
1 u + 19 |
3 u + 18 |
3 u - 18 |
Change |
+ 19 |
- 19 |
- 18 |
+ 18 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Min gives Ben some money or Ben gives Min some money, the total amount of money remains the same.
Total amount that Ben and Min have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Ben and Min each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Ben has at first in Case 1 and Case 2 is the same.
5 u - 19 = 3 u + 18
5 u - 3 u = 18 + 19
1 u = 37
Amount that Ben has
= 3 u + 18
= 3 x 37 + 18
= 111 + 18
= $129
(b)
Amount that Min has
= 1 u + 19
= 37 + 19
= $56
Answer(s): (a) $129; (b) $56