Tim's current age is 9 times as old as John's age years ago. Today, John's age is Tim's age the same number of years ago. How old is John's age now if the total of their current age is 56?
| |
Tim |
John |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
9 u |
1 p |
9 u - 1 p |
56 |
Total age of Tim and John today = 9 u + 1 p
9 u + 1 p = 56 --- (1)
The difference in Tim's age and John'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 = 56
9 u + 5 u = 56
14 u = 56
1 u = 56 ÷ 14 = 4
Tim's age now
= 56 - 9 u
= 56 - 9 x 4
= 56 - 36
= 20
Answer(s): 20
