Liam's current age is 7 times as old as Vincent's age years ago. Today, Vincent's age is Liam's age the same number of years ago. How old is Vincent's age now if the total of their current age is 77?
| |
Liam |
Vincent |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
7 u |
1 p |
7 u - 1 p |
77 |
Total age of Liam and Vincent today = 7 u + 1 p
7 u + 1 p = 77 --- (1)
The difference in Liam's age and Vincent'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 = 77
7 u + 4 u = 77
11 u = 77
1 u = 77 ÷ 11 = 7
Liam's age now
= 77 - 7 u
= 77 - 7 x 7
= 77 - 49
= 28
Answer(s): 28
