Caden's current age is 5 times as old as David's age years ago. Today, David's age is Caden's age the same number of years ago. How old is David's age now if the total of their current age is 32?
| |
Caden |
David |
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 Caden and David today = 5 u + 1 p
5 u + 1 p = 32 --- (1)
The difference in Caden's age and David'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
Caden's age now
= 32 - 5 u
= 32 - 5 x 4
= 32 - 20
= 12
Answer(s): 12
