Archie's current age is 5 times as old as Sam's age years ago. Today, Sam's age is Archie's age the same number of years ago. How old is Sam's age now if the total of their current age is 72?
| |
Archie |
Sam |
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 Sam today = 5 u + 1 p
5 u + 1 p = 72 --- (1)
The difference in Archie's age and Sam'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
= 72 - 5 u
= 72 - 5 x 9
= 72 - 45
= 27
Answer(s): 27
