John's current age is 5 times as old as Seth's age years ago. Today, Seth's age is John's age the same number of years ago. How old is John's age now if the total of their current age is 24?
| |
John |
Seth |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
5 u |
1 p |
5 u - 1 p |
24 |
Total age of John and Seth today = 5 u + 1 p
5 u + 1 p = 24 --- (1)
The difference in John's age and Seth'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 = 24
5 u + 3 u = 24
8 u = 24
1 u = 24 ÷ 8 = 3
John's age now
= 5 u
= 5 x 3
= 15
Answer(s): 15
