Ken and Mark have some money. If Ken gives $283 to Mark, the ratio of their money will be 2 : 5. If Ken gives $454 to Mark, the ratio of their money will be 1: 4. How much does Ken have?
|
Case 1 |
Case 2 |
|
Ken |
Mark |
Ken |
Mark |
Before |
10 u + $283 |
25 u - $283 |
7 u + $454 |
28 u - $454 |
Change |
- $283 |
+ $283 |
- $454 |
+ $454 |
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 + 283 = 7 u + 454
10 u - 7 u = 454 - 283
3 u = 171
1 u = 171 ÷ 3 = 57
Amount that Ken has
= 10 u + 283
= 10 x 57 + 283
= 570 + 283
= $853
Answer(s): $853