Luke's current age is 3 times as old as Michael's age years ago. Today, Michael's age is Luke's age the same number of years ago. How old is Michael's age now if the total of their current age is 40?
| |
Luke |
Michael |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
3 u |
1 p |
3 u - 1 p |
40 |
Total age of Luke and Michael today = 3 u + 1 p
3 u + 1 p = 40 --- (1)
The difference in Luke's age and Michael's age remains the same.
3 u - 1 p = 1 p - 1 u
3 u + 1 u = 1 p + 1 p
4 u = 2 p
2 u = 1 p
Substitute 1 p = 2 u into (1).
3 u + 1 p = 40
3 u + 2 u = 40
5 u = 40
1 u = 40 ÷ 5 = 8
Luke's age now
= 40 - 3 u
= 40 - 3 x 8
= 40 - 24
= 16
Answer(s): 16
