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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.
 

Return to Basic Algebra - Lesson 3  Click Here


 
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