SOLUTION: If {{{x=1+(1/2)+(1/4)+(1/8)}}} and {{{a=1+(1/2)x}}}, then a is how much larger than x? A) 1/48 B) 1/16 C) 3/16 D) 15/16

Algebra ->  Expressions -> SOLUTION: If {{{x=1+(1/2)+(1/4)+(1/8)}}} and {{{a=1+(1/2)x}}}, then a is how much larger than x? A) 1/48 B) 1/16 C) 3/16 D) 15/16      Log On


   

Question 1042934: If x=1%2B%281%2F2%29%2B%281%2F4%29%2B%281%2F8%29 and a=1%2B%281%2F2%29x, then a is how much larger than x?
A) 1/48
B) 1/16
C) 3/16
D) 15/16
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's simplify the expression for x.


x=1%2B%281%2F2%29%2B%281%2F4%29%2B%281%2F8%29


x=8%2F8%2B4%2F8%2B2%2F8%2B1%2F8


x=%288%2B4%2B2%2B1%29%2F8


x=15%2F8


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Now plug x=15%2F8 into the equation for 'a'


a=1%2B%281%2F2%29%2Ax


a=1%2B%281%2F2%29%2A%2815%2F8%29 Replace x with 15/8


a=1%2B%281%2A15%29%2F%282%2A8%29


a=1%2B15%2F16


a=16%2F16%2B15%2F16


a=%2816%2B15%29%2F16


a=31%2F16


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We now know the values of "a" and "x". Let's subtract them.


a-x+=+31%2F16-15%2F8


a-x+=+31%2F16-30%2F16


a-x+=+%2831-30%29%2F16


a-x+=+1%2F16


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The final answer is choice B) 1/16