George's current age is 7 times as old as Luke's age years ago. Today, Luke's age is George's age the same number of years ago. How old is George's age now if the total of their current age is 22?
|
George |
Luke |
Difference |
Total |
Before |
1 p |
1 u |
1 p - 1 u |
|
Change |
+ ? |
+ ? |
|
|
After |
7 u |
1 p |
7 u - 1 p |
22 |
Total age of George and Luke today = 7 u + 1 p
7 u + 1 p = 22 --- (1)
The difference in George's age and Luke'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 = 22
7 u + 4 u = 22
11 u = 22
1 u = 22 ÷ 11 = 2
George's age now
= 7 u
= 7 x 2
= 14
Answer(s): 14