Question 538599
Bob is one third the age of his father. In 12 years he will be half the age of his father. How old is each now?


Let F = age of the father
Let B = age of Bob


The information provided:


B = F/3. This is the Equation 1.


B+12 = Bob's age in 12 years
F+12 = Father's age in 12 years


So, 


B+12 = (F+12)/2. 


B+12 = (F+12)/2


Let's simplify this equation.


In order to remove the 2 in the denominator, let's multiply both sides of the equation by 2.


(B+12)*2 = 2*(F+12)/2
2B+12*2 = (F+12)
2B+24 = F+12


Subtract 12 from both sides of the equation.


2B+24-12 = F+12-12
2B+12 = F+0


Subtract  2B from  both sides of the equation.


2B+12 -2B = F+0-2B
0+12 = F-2B


12 = F-2B. This is the Equation 2.



Now, we must substitute the Equation 1 (B=F/3) into the Equation 2 (12 = F-2B):



12 = F-2B 
12 = F- 2*(F/3)
12 = F- (2F/3)
12 = (3F -2F)/3
12 = F/3


Multiply both sides of the equation by 3:



12*3 = 3*F/3

36 = F. 


Now, we must substitute the value of F = 36 into the Equation 1 (B=F/3)


B=F/3
B=36/3
B=12



The answers are:



The father's age is 36
Bob's age is 12


If you have some questions, please feel free to let me know.