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You are HERE >> Mathematics > Algebra > Grade 9

Answer Key To Basic Algebra - Lesson 3

If x is George's age, then x - 4 is Jon's age because George is 4 years older than Jon. George is 8 years older than Jim, making Jim's age x - 8. George is 12 years older than Sam, so Sam's age can be represented as 
x - 12. 

             We also know that Sam is 1/2 the age of George.

             So, set up the expression:

             (x - 12) = 1/2 x

To solve for x, you first need to put 1/2x into a different form. 
Multiply 1/2 by x. 

 x is the same as x over 1 if you put it into fraction form, or x/1. So, when you multiply 1/2 by x, it would actually look like (1/2) (x/1). When you multiply fractions, you multiply the numerators (1)(x) and then the denominators (2)(1). The result is x/2. Now rewrite the expression using x/2 instead of 1/2x.

             (x-12) = x/2

 We learned that when you solve an expression, you want to "isolate" the variable. To do this, multiply BOTH sides by 2.

             (x-12) = x/2

           2(x-12) = 2(x/2)

             2x -24 = x

 Now, you need to get both variables on the same side of the equal sign, so subtract 2x from BOTH sides:

             2x - 2x - 24 = x - 2x

                         -24 = -1x (Divide -24 by -1 to solve for x)

                          24 = x

 therefore, George is 24. Jon's age is represented by x - 4 or 20. 
Jim is x - 8, or 16. And Sam is x - 12, or 12.
You can further check the problem by multiplying Sam's age by 2, to get George's age, because the problem told us that Sam is half the age of George.

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