Luis's current age is 9 times as old as Gabriel's age years ago. Today, Gabriel's age is Luis's age the same number of years ago. How old is Luis's age now if the total of their current age is 112?
| |
Luis |
Gabriel |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
9 u |
1 p |
9 u - 1 p |
112 |
Total age of Luis and Gabriel today = 9 u + 1 p
9 u + 1 p = 112 --- (1)
The difference in Luis's age and Gabriel's age remains the same.
9 u - 1 p = 1 p - 1 u
9 u + 1 u = 1 p + 1 p
10 u = 2 p
5 u = 1 p
Substitute 1 p = 5 u into (1).
9 u + 1 p = 112
9 u + 5 u = 112
14 u = 112
1 u = 112 ÷ 14 = 8
Luis's age now
= 9 u
= 9 x 8
= 72
Answer(s): 72
