Archie's current age is 5 times as old as Owen's age years ago. Today, Owen's age is Archie's age the same number of years ago. How old is Archie's age now if the total of their current age is 72?
| |
Archie |
Owen |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
5 u |
1 p |
5 u - 1 p |
72 |
Total age of Archie and Owen today = 5 u + 1 p
5 u + 1 p = 72 --- (1)
The difference in Archie's age and Owen'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 = 72
5 u + 3 u = 72
8 u = 72
1 u = 72 ÷ 8 = 9
Archie's age now
= 5 u
= 5 x 9
= 45
Answer(s): 45
