Question

The cost of 300 metres optic fibre is $200 what will be the cost if 1 metre of optic fibre.

Answer 1

The answer is:  " $0.67 / metre " ;  
                        or, write as:  " [ $\frac{2}{3}$ dollar] per metre."
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Step-by-step explanation:

This is a unit rate problem:
   Find the cost in dollars per [single unit—in this case: "metre(s)", "m" ;
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 $\frac{200 dollars}{300m} = \frac{? dollars}{1m}$ ;  Solve for the "?" amount of dollars.
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Method 1)  "Cross-factor multiply" :
Note:  Given: " $\frac{a}{b} = \frac{c}{d} ; [b\neq 0; d\neq 0]$ " ;

 then:   ⟷  " $ad = bc$ " ;
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So:  " \frac{200 dollars}{300m} = \frac{? dollars}{1m} " ;

  then:   ⟷  " (200*1) = (300* ?) ;

     → "  (200) = (300  * ?)" ;

     ↔ " (300 * ?) = 200 " ;  

Let "x" refer to the "?" ; the "unknown value" (in dollars);

                for which we are trying to solve.

⇒ " 300x = 200 " ;  Solve for "x" ;
     → Divide each side of the equation by: "300" ;

       to isolate "x" on the "left-hand side" of the equation; & to              solve  for "x" ;
   ⇒  300x/ 300 = 200/300 ;

    To get:  " x = $\frac{2}{3}$ dollars" ;  

= $0.666666666... ;

round to: $0.67 .

{since: " 1 dollar = $1.00 = 100 cents" ;
and since: "\frac{2}{3} " ;

= ["2 ÷ 3" = 0.666666...." ] ;  

⇒  round to:  "0.67 " ;  

and write as:
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⇒  $0.67 / metre ;   or, write as:
    " [ $\frac{2}{3}$ dollar] per metre."
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Method 2)  Note:
\frac{200 dollars}{300m} = \frac{? dollars}{1m} ;

⇔   = "  $\frac{200}{300}$  $\frac{dollars}{metre}$ " ;
      {Note:  "[200÷300]" can be simplified by "canceling out" the two (2) zeros in both the numerator and the denominator.}.

   = " \frac{2 dollars}{3m} ";
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  =  i.e. " $\frac{\frac{2}{3} dollars}{metre}$ " or;  $\frac{0.67 dollars} {m}$ ;  or:  $0.67 / metre .

         ⇒  {since:  " $\frac{2}{3}$ of 1 dollar" = " \frac{2}{3} dollars of 100 cents" ;
        ⇒  {since:  "1 dollar = 100 cents"} ;

           ⇒ {and: " $\frac{2}{3}$ " = 0.6666666666666... " } ;  

 → round to:  "0.67 " ; and thus: $0.67 / metre.
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Note that using either of these 2 (two) methods result in the same answer.
               Hope this is helpful!  Best wishes to you within your academic pursuits!
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