Question 1164624
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Let me use the work you show to demonstrate what gives beginning algebra students difficulty in setting up problems for solving using algebra.<br>
Here is what you say:<br>
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.<br>
In your first line, you use the first sentence of the problem to define expressions for the ages of Raymond and Susan.  Good start.<br>
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.<br>
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.<br>
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.<br>
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:<br>
{{{x-4 = 4(x-16)}}}
{{{x-4 = 4x-64}}}
{{{60 = 3x}}}
{{{x = 20}}}<br>
ANSWER: Susan's age is x=20; Raymond's age is x-12 = 8.<br>
CHECK: 4 years ago Susan was 16 and Raymond was 4; 16 is 4 times 4.<br>