SOLUTION: 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?

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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?
Answer by Mathpassionate(25) About Me  (Show Source):
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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.