Ken and Fred have some money. If Ken gives $203 to Fred, the ratio of their money will be 2 : 5. If Ken gives $473 to Fred, the ratio of their money will be 1: 4. How much does Ken have?
|
Case 1 |
Case 2 |
|
Ken |
Fred |
Ken |
Fred |
Before |
10 u + $203 |
25 u - $203 |
7 u + $473 |
28 u - $473 |
Change |
- $203 |
+ $203 |
- $473 |
+ $473 |
After
|
2x5 = 10 u |
5x5 = 25 u |
1x7 = 7 u |
4x7 = 28 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 7 and 5 is 35.
The amount that Ken has at first is the same in both cases.
10 u + 203 = 7 u + 473
10 u - 7 u = 473 - 203
3 u = 270
1 u = 270 ÷ 3 = 90
Amount that Ken has
= 10 u + 203
= 10 x 90 + 203
= 900 + 203
= $1103
Answer(s): $1103