Liam's current age is 9 times as old as Ben's age years ago. Today, Ben's age is Liam's age the same number of years ago. How old is Ben's age now if the total of their current age is 42?
| |
Liam |
Ben |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
9 u |
1 p |
9 u - 1 p |
42 |
Total age of Liam and Ben today = 9 u + 1 p
9 u + 1 p = 42 --- (1)
The difference in Liam's age and Ben'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 = 42
9 u + 5 u = 42
14 u = 42
1 u = 42 ÷ 14 = 3
Liam's age now
= 42 - 9 u
= 42 - 9 x 3
= 42 - 27
= 15
Answer(s): 15
