Perry's current age is 7 times as old as Liam's age years ago. Today, Liam's age is Perry's age the same number of years ago. How old is Liam's age now if the total of their current age is 55?
| |
Perry |
Liam |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
7 u |
1 p |
7 u - 1 p |
55 |
Total age of Perry and Liam today = 7 u + 1 p
7 u + 1 p = 55 --- (1)
The difference in Perry's age and Liam's age remains the same.
7 u - 1 p = 1 p - 1 u
7 u + 1 u = 1 p + 1 p
8 u = 2 p
4 u = 1 p
Substitute 1 p = 4 u into (1).
7 u + 1 p = 55
7 u + 4 u = 55
11 u = 55
1 u = 55 ÷ 11 = 5
Perry's age now
= 55 - 7 u
= 55 - 7 x 5
= 55 - 35
= 20
Answer(s): 20
