SOLUTION: Raymond is 12 years younger than Susan. Four years ago, she was 4 times as old as he was. Find their present ages. I know that right now, Susan is x and Raymond is x-12. 4

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Question 1164624: Raymond is 12 years younger than Susan. Four years ago, she was 4 times as old as he was. Find their present ages.
I know that right now, Susan is x and Raymond is x-12. 4 years ago, Susan is 4(x-12). I'm not sure how to set the problem up after this. Please help. TY!
Found 3 solutions by Alan3354, ikleyn, greenestamps:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Raymond is 12 years younger than Susan. Four years ago, she was 4 times as old as he was. Find their present ages.
------------------
4 years ago, he was 12 years younger.
-----
4 rears ago:
R = S - 12
S = 4R
--
R = 4R-12
R = 4
S = 16
====================
Now:
R = 8
S = 20
Answer by ikleyn(52855)   (Show Source): You can put this solution on YOUR website!
.

            I will start as you do,  and then will continue as it  SHOULD  BE. 


Let x be the Susan age.

Then the Raymond's age is (x-12), according to the condition.


Four years ago, Susan was (x-4) years old.

Four years ago, Raymond was ((x-12)-4) = x - 16 years old.



    +----------------------------------------------------------+
    |   "Four years ago, she was 4 times as old as he was."    |
    +----------------------------------------------------------+



It means that


    x - 4 = 4*(x-16).    <<<---===  it is your setup equation.

                                    You take it from the condition, using the introduced variables.


Now you have this single equation and simplify it step by step


    x - 4  = 4x - 64

    64 - 4 = 4x - x

    60     = 3x

     x = 20.


ANSWER.  Susan is 20 years old now.  Raymond is 12 years younger, i.e. 20=12 = 8 years old.

Solved.

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

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    - Age problems and their solutions
    - 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
    - Miscellaneous age problems
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Read them and become an expert in solving age problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - 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

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Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Let me use the work you show to demonstrate what gives beginning algebra students difficulty in setting up problems for solving using algebra.

Here is what you say:

I know that right now, Susan is x and Raymond is x-12.
4 years ago, Susan is 4(x-12).
I'm not sure how to set the problem up after this.

In your first line, you use the first sentence of the problem to define expressions for the ages of Raymond and Susan. Good start.

In the second line, you try to use the statement that 4 years ago she was 4 times as he was then; unfortunately, the equation you write says that her age 4 years ago was 4 times as old as he is NOW.

The step that a lot of beginning students skip is this: the second sentence of the problem talks about their ages 4 years ago -- so you need to find expressions for those.

So, given your definitions of their current ages, you need to note (i.e., write on the paper on which you are working on the problem!) that their ages 4 years ago were x-4 for Susan and (x-12)-4 = x-16 for Raymond.

NOW you have expressions for both their ages 4 years ago; so now you can write the equation that says 4 years ago Susan's age was 4 times Raymond's age:






ANSWER: Susan's age is x=20; Raymond's age is x-12 = 8.

CHECK: 4 years ago Susan was 16 and Raymond was 4; 16 is 4 times 4.
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