What is the process to write an equation to solve this problem?

Question

Al and Fred's ages total 48. Al is twice as old as Fred will be when  Fred is three times as old as Al was when Al was three times as old as Fred. How old is Al?                                                                                                     

Answer 1

Al is dead!

Answer 2

Hi Mike, we need to set up two equations. Let x represent Al's age and y represent Fred's age. The first equation would represent the total of their ages:

 

x + y = 48

 

The second equation will represent the future and past ages of Al and Fred.

 

x + 2y = 9y

 

This represents Al being 2 times as old as Fred when Fred is 3 times as old as Al when Al was 3 times as old as Fred.

 

Think of a table like this

 

y     3x    9y

---------------

1      3      9

2      6    18

3      9    27

4     12   36

5     15   45

6     18   54

 

Solve:

 

x   +    y  =  48

x   +  2y  =  9y

------------------

 

Subtract 9y from both sides of equation 2:

 

x   +   y = 48
x   -  7y =   0

----------------

 

Multiply the second row by -1 and subtract:

 

 x +  y = 48
-x + 7y = 0

--------------

 

        8y = 48

 

Divide by 8:

 

y = 6

 

Substitute into equation 1 to find Al's age.

 

x  + 6  = 48

 

Subtract 6 from both sides:

 

x = 42

 

Al's age is 42 and Fred's age is 6.

 

Check:

 

42 + 6  = 48

 

42 + 2 * 6 = 9 * 6

 

42 + 12 = 54

 

54  =  54, values check.

 

Questions?

 

 

 

 

Answer 3

Mike,  Here is how I would figure out the ages.   You are given the first equation and get the second from the additional information.  

 

A + F = 48

 

A = 3F  substitute back into first equation:  3F + F = 48 solve for F 

4F = 48

F= 12  substitute back into first:

 

A + 12 = 48

 

A = 36 years old while F = 12.  

 

Hope this helps!