Caden's current age is 7 times as old as Jack's age years ago. Today, Jack's age is Caden's age the same number of years ago. How old is Jack's age now if the total of their current age is 55?
| |
Caden |
Jack |
Difference |
Total |
| Before |
1 p |
1 u |
1 p - 1 u |
|
| Change |
+ ? |
+ ? |
|
|
| After |
7 u |
1 p |
7 u - 1 p |
55 |
Total age of Caden and Jack today = 7 u + 1 p
7 u + 1 p = 55 --- (1)
The difference in Caden's age and Jack's age remains the same.
7 u - 1 p = 1 p - 1 u
7 u + 1 u = 1 p + 1 p
8 u = 2 p
4 u = 1 p
Substitute 1 p = 4 u into (1).
7 u + 1 p = 55
7 u + 4 u = 55
11 u = 55
1 u = 55 ÷ 11 = 5
Caden's age now
= 55 - 7 u
= 55 - 7 x 5
= 55 - 35
= 20
Answer(s): 20
