Michael's current age is 9 times as old as Ethan's age years ago. Today, Ethan's age is Michael's age the same number of years ago. How old is Michael's age now if the total of their current age is 28?
| |
Michael |
Ethan |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
9 u |
1 p |
9 u - 1 p |
28 |
Total age of Michael and Ethan today = 9 u + 1 p
9 u + 1 p = 28 --- (1)
The difference in Michael's age and Ethan'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 = 28
9 u + 5 u = 28
14 u = 28
1 u = 28 ÷ 14 = 2
Michael's age now
= 9 u
= 9 x 2
= 18
Answer(s): 18
