Simon's current age is 5 times as old as Mark's age years ago. Today, Mark's age is Simon's age the same number of years ago. How old is Mark's age now if the total of their current age is 56?
| |
Simon |
Mark |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
5 u |
1 p |
5 u - 1 p |
56 |
Total age of Simon and Mark today = 5 u + 1 p
5 u + 1 p = 56 --- (1)
The difference in Simon's age and Mark's age remains the same.
5 u - 1 p = 1 p - 1 u
5 u + 1 u = 1 p + 1 p
6 u = 2 p
3 u = 1 p
Substitute 1 p = 3 u into (1).
5 u + 1 p = 56
5 u + 3 u = 56
8 u = 56
1 u = 56 ÷ 8 = 7
Simon's age now
= 56 - 5 u
= 56 - 5 x 7
= 56 - 35
= 21
Answer(s): 21
