Vincent's current age is 9 times as old as Paul's age years ago. Today, Paul's age is Vincent's age the same number of years ago. How old is Paul's age now if the total of their current age is 140?
| |
Vincent |
Paul |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
9 u |
1 p |
9 u - 1 p |
140 |
Total age of Vincent and Paul today = 9 u + 1 p
9 u + 1 p = 140 --- (1)
The difference in Vincent's age and Paul'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 = 140
9 u + 5 u = 140
14 u = 140
1 u = 140 ÷ 14 = 10
Vincent's age now
= 140 - 9 u
= 140 - 9 x 10
= 140 - 90
= 50
Answer(s): 50
