what is the answer

Question

Teresa is thinking of a fraction. She says 1/8 more than 1/2 of her fraction is equal to 7/8 less than twice her fractio. What fraction is Tesera thinking of?

 

Answer 1

Let x = the fraction

 

Translate

"/8 more than 1/2 of her fraction is equal to 7/8 less than twice her fraction'       means

    1/8   +    (1/2)*x                        =     (  -(7/8)    +      2*x  }

 

Rewrite:

 

    x/2 + 1/8 = 2x - 7/8              [by convention, write x values first]

    4x + 1 = 16x - 7                    [multiply by LCM=8 to get rid of fraction]

        -12x = -8  

            x = 2/3                      [divide by -12]

 

Check:

    Is   (1/2)(2/3) + 1/8 = (2)(2/3) - 7/8    ?

               1/3      + 1/8  =   4/3   -   7/8    ?

               8/24   +  3/24  =   32/24  -  21/24   ?

                      11/24   =  11/24   ?yes