Sam's current age is 5 times as old as Liam's age years ago. Today, Liam's age is Sam's age the same number of years ago. How old is Sam's age now if the total of their current age is 16?
| |
Sam |
Liam |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
5 u |
1 p |
5 u - 1 p |
16 |
Total age of Sam and Liam today = 5 u + 1 p
5 u + 1 p = 16 --- (1)
The difference in Sam's age and Liam's age remains the same.
5 u - 1 p = 1 p - 1 u
5 u + 1 u = 1 p + 1 p
6 u = 2 p
3 u = 1 p
Substitute 1 p = 3 u into (1).
5 u + 1 p = 16
5 u + 3 u = 16
8 u = 16
1 u = 16 ÷ 8 = 2
Sam's age now
= 5 u
= 5 x 2
= 10
Answer(s): 10
