Ken's current age is 5 times as old as Vincent's age years ago. Today, Vincent's age is Ken's age the same number of years ago. How old is Ken's age now if the total of their current age is 32?
| |
Ken |
Vincent |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
5 u |
1 p |
5 u - 1 p |
32 |
Total age of Ken and Vincent today = 5 u + 1 p
5 u + 1 p = 32 --- (1)
The difference in Ken's age and Vincent's age remains the same.
5 u - 1 p = 1 p - 1 u
5 u + 1 u = 1 p + 1 p
6 u = 2 p
3 u = 1 p
Substitute 1 p = 3 u into (1).
5 u + 1 p = 32
5 u + 3 u = 32
8 u = 32
1 u = 32 ÷ 8 = 4
Ken's age now
= 5 u
= 5 x 4
= 20
Answer(s): 20
