1/3÷reciprocal of a particular number,result is 8 less than the number.

Question

When 1/3 is divided by the reciprocal of a particular number,the result is 8 less than the number the number is which of the following 

3

6

8

9

12

Answer 1

You can set this up as an equation.  First, you must know that a reciprocal is 1/number.  So if your number is unknown, and we call it x, the reciprocal is 1/x.

 

(1/3)/(1/x) = x-8 (This turns the words into an actual equation)

 

(1/3)*(x/1) = x-8 (To divide fractions, "flip" the second one, and multiply instead)

 

x/3 = x-8

 

x = 3x-24 (multiply every term by 3)

24 = 2x (subtract x from both sides, and add 24 to both sides)

12 = x (divide by 2)