Ken's current age is 5 times as old as Xavier's age years ago. Today, Xavier'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 56?
| |
Ken |
Xavier |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
5 u |
1 p |
5 u - 1 p |
56 |
Total age of Ken and Xavier today = 5 u + 1 p
5 u + 1 p = 56 --- (1)
The difference in Ken's age and Xavier'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 = 56
5 u + 3 u = 56
8 u = 56
1 u = 56 ÷ 8 = 7
Ken's age now
= 5 u
= 5 x 7
= 35
Answer(s): 35
