Valen's current age is 9 times as old as Nick's age years ago. Today, Nick's age is Valen's age the same number of years ago. How old is Nick's age now if the total of their current age is 140?
| |
Valen |
Nick |
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 Valen and Nick today = 9 u + 1 p
9 u + 1 p = 140 --- (1)
The difference in Valen's age and Nick'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
Valen's age now
= 140 - 9 u
= 140 - 9 x 10
= 140 - 90
= 50
Answer(s): 50
