Liam's current age is 9 times as old as Owen's age years ago. Today, Owen's age is Liam's age the same number of years ago. How old is Owen's age now if the total of their current age is 112?
| |
Liam |
Owen |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
9 u |
1 p |
9 u - 1 p |
112 |
Total age of Liam and Owen today = 9 u + 1 p
9 u + 1 p = 112 --- (1)
The difference in Liam's age and Owen'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 = 112
9 u + 5 u = 112
14 u = 112
1 u = 112 ÷ 14 = 8
Liam's age now
= 112 - 9 u
= 112 - 9 x 8
= 112 - 72
= 40
Answer(s): 40
