Liam's current age is 5 times as old as Ivan's age years ago. Today, Ivan's age is Liam's age the same number of years ago. How old is Ivan's age now if the total of their current age is 56?
| |
Liam |
Ivan |
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 Liam and Ivan today = 5 u + 1 p
5 u + 1 p = 56 --- (1)
The difference in Liam's age and Ivan'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
Liam's age now
= 56 - 5 u
= 56 - 5 x 7
= 56 - 35
= 21
Answer(s): 21
