SOLUTION: John is 43 years old and his daughter Susan is 7. In n-years, John will be four times as old as Susan is at that point. Find n and the ages of John and Susan after n-years.

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Question 1174209: John is 43 years old and his daughter Susan is 7. In n-years, John will be four times as old as Susan is at that point. Find n and the ages of John and Susan after n-years.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.

Write the equation for their ages in n years


    43 + n = 4*(7 + n).


Now solve it


    43 + n = 28 + 4n

    43 - 28 = 4n - n

      15    = 3n

       n    = 15/3 = 5.


Answer.   a)  n= 5:  in 5 years.

          b)  At that time, they will be  48 (the father) and 12 (Susan) years old.

Solved.

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There is a bunch of lessons on age word problems
    - Age problems and their solutions
    - HOW TO algebreze and to solve age problems?
    - A fresh formulation of a traditional age problem
    - Really intricate age word problems
    - Selected age word problems from the archive
    - Age problems for mental solution
    - Age problem for three participants
    - Miscellaneous age problems
in this site.

Read them and become an expert in solving age problems.

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    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Age word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

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


The other tutor showed a typical formal algebraic solution; you should certainly understand that method and know how to use it.

Here is a less formal path to the solution using logical reasoning. Solving a problem like this can give you very beneficial mental exercise.

(1) The difference in their ages is (and always will be) 43-7 = 36 years.
(2) When John is 4 times as old as his daughter, the difference in their ages will be 3 times her age. (If we want to use a bit of very basic algebra here, we are saying 4x-x = 3x.)
(3) So when John is 4 times as old as his daughter, 3x=36 so x=12.

That means he will be 4 times as old as her when she is 12 and he is 4*12 = 48.

Since their ages are now 43 and 7, that will be 5 years from now.

ANSWERS: 5 years from now their ages will be 12 and 48.
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