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