Ethan's current age is 7 times as old as Ken's age years ago. Today, Ken's age is Ethan's age the same number of years ago. How old is Ken's age now if the total of their current age is 66?
|
Ethan |
Ken |
Difference |
Total |
Before |
1 p |
1 u |
1 p - 1 u |
|
Change |
+ ? |
+ ? |
|
|
After |
7 u |
1 p |
7 u - 1 p |
66 |
Total age of Ethan and Ken today = 7 u + 1 p
7 u + 1 p = 66 --- (1)
The difference in Ethan's age and Ken's age remains the same.
7 u - 1 p = 1 p - 1 u
7 u + 1 u = 1 p + 1 p
8 u = 2 p
4 u = 1 p
Substitute 1 p = 4 u into (1).
7 u + 1 p = 66
7 u + 4 u = 66
11 u = 66
1 u = 66 ÷ 11 = 6
Ethan's age now
= 66 - 7 u
= 66 - 7 x 6
= 66 - 42
= 24
Answer(s): 24