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