Archie's current age is 9 times as old as Ryan's age years ago. Today, Ryan'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 98?
|
Archie |
Ryan |
Difference |
Total |
Before |
1 p |
1 u |
1 p - 1 u |
|
Change |
+ ? |
+ ? |
|
|
After |
9 u |
1 p |
9 u - 1 p |
98 |
Total age of Archie and Ryan today = 9 u + 1 p
9 u + 1 p = 98 --- (1)
The difference in Archie's age and Ryan'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 = 98
9 u + 5 u = 98
14 u = 98
1 u = 98 ÷ 14 = 7
Archie's age now
= 9 u
= 9 x 7
= 63
Answer(s): 63