Tim's current age is 5 times as old as Caden's age years ago. Today, Caden's age is Tim's age the same number of years ago. How old is Caden's age now if the total of their current age is 40?
| |
Tim |
Caden |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
5 u |
1 p |
5 u - 1 p |
40 |
Total age of Tim and Caden today = 5 u + 1 p
5 u + 1 p = 40 --- (1)
The difference in Tim's age and Caden'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 = 40
5 u + 3 u = 40
8 u = 40
1 u = 40 ÷ 8 = 5
Tim's age now
= 40 - 5 u
= 40 - 5 x 5
= 40 - 25
= 15
Answer(s): 15
