SOLUTION: John is five times as old as his brother. The difference between their age is twelve years. What is John age?

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Question 1200692: John is five times as old as his brother. The difference between their age is twelve years. What is John age?
Found 4 solutions by Theo, ikleyn, MathTherapy, greenestamps:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
j = john's age.
b = his brother's age.
j = 5b
j - b = 12
replace j with 5 b in the second equation to get:
5b - b = 12
combine like terms to get:
4b = 12
solve for b to get:
b = 12/4 = 3
j = 5b gets you j = 15
j - b = 12 gets you j - 3 = 12 which gets you j = 3 + 12 which gets you j = 15 again.
your solution is that john is 15 and his brother is 3.
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

Let x be the brother's age;  then the John's age is 5x, years, according to the problem.


The difference of ages is 12 years

    5x - x = 12,

or

      4x   = 12,

       x   = 12/4 = 3.


The brother is 3 years old;  John is 3*5 = 15 years old.


ANSWER.  John is 15 years old.

Solved.

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This solution is so easy . . .

You even may re-tell this solution in words - - - then you will get the MENTAL version of the solution.



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
John is five times as old as his brother. The difference between their age is twelve years. What is John age?

Let John's and the brother's ages be J and B, respectively
Then we get: J = 5B ----- eq (i)
As John is older, we also get: J - B = 12___J - 12 = B ----- eq (ii)
               J = 5(J - 12) ----- Substituting J - 12 for B in eq (i)
               J = 5J - 60
          J - 5J = - 60
            - 4J = - 60
John's age or

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


You can get good mental exercise and problem-solving experience by solving the problem informally, using logical reasoning and simple arithmetic instead of algebra -- as tutor @ikleyn suggests in her response.

If John is 5 times as old as his brother, then the difference in their ages is 4 times the brother's age.
But the difference in their ages is given to be 12 years.
Therefore the brother's age is 12/4 = 3.
And that makes John's age 5*3 = 15.

ANSWER: 15

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And, by the way....

If you are going to use formal algebra, using a single variable as tutor @ikleyn does is FAR easier than using two variables, as the other tutors did.
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