Liam's current age is 7 times as old as Howard's age years ago. Today, Howard's age is Liam's age the same number of years ago. How old is Howard's age now if the total of their current age is 55?
| |
Liam |
Howard |
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 Liam and Howard today = 7 u + 1 p
7 u + 1 p = 55 --- (1)
The difference in Liam's age and Howard'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
Liam's age now
= 55 - 7 u
= 55 - 7 x 5
= 55 - 35
= 20
Answer(s): 20
