Pierre's current age is 9 times as old as David's age years ago. Today, David's age is Pierre's age the same number of years ago. How old is Pierre's age now if the total of their current age is 84?
| |
Pierre |
David |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
9 u |
1 p |
9 u - 1 p |
84 |
Total age of Pierre and David today = 9 u + 1 p
9 u + 1 p = 84 --- (1)
The difference in Pierre's age and David'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 = 84
9 u + 5 u = 84
14 u = 84
1 u = 84 ÷ 14 = 6
Pierre's age now
= 9 u
= 9 x 6
= 54
Answer(s): 54
