Sam's current age is 9 times as old as Archie's age years ago. Today, Archie's age is Sam's age the same number of years ago. How old is Archie's age now if the total of their current age is 112?
| |
Sam |
Archie |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
9 u |
1 p |
9 u - 1 p |
112 |
Total age of Sam and Archie today = 9 u + 1 p
9 u + 1 p = 112 --- (1)
The difference in Sam's age and Archie's age remains the same.
9 u - 1 p = 1 p - 1 u
9 u + 1 u = 1 p + 1 p
10 u = 2 p
5 u = 1 p
Substitute 1 p = 5 u into (1).
9 u + 1 p = 112
9 u + 5 u = 112
14 u = 112
1 u = 112 ÷ 14 = 8
Sam's age now
= 112 - 9 u
= 112 - 9 x 8
= 112 - 72
= 40
Answer(s): 40
