Dana and Min have some money. If Dana spends $2, she will have
45 as much money as Min. If Min spends $3, Dana will have
67 as much money as Min. How much money does Min have?
| |
Case 1 |
Case 2 |
| |
Dana |
Min |
Dana |
Min |
| Before |
4 u + $2 |
5 u |
6 p |
7 p + $3 |
| Change |
- $2 |
|
|
- $3 |
| After |
4 u |
5 u |
6 p |
7 p |
The amount that Dana has at first in Case 1 and Case 2 is the same.
4 u + 2 = 6 p
4 u = 6 p - 2 --- (1)
The amount that Min has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 3 --- (2)
Make u the same.
(1)
x 520 u = 30 p - 10 --- (3)
(2)
x 420 u = 28 p + 12 --- (4)
(3) = (4)
30 p - 10 = 28 p + 12
30 p - 28 p = 10 + 12
2 p = 22
1 p = 22 ÷ 2 = 11
Amount that Min has
= 7 p + 3
= 7 x 11 + 3
= 77 + 3
= $80
Answer(s): $80
