Gabriel's current age is 7 times as old as Ryan's age years ago. Today, Ryan's age is Gabriel's age the same number of years ago. How old is Ryan's age now if the total of their current age is 22?
| |
Gabriel |
Ryan |
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 Gabriel and Ryan today = 7 u + 1 p
7 u + 1 p = 22 --- (1)
The difference in Gabriel's age and Ryan'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
Gabriel's age now
= 22 - 7 u
= 22 - 7 x 2
= 22 - 14
= 8
Answer(s): 8
