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: " [
`(2)/(3)` dollar] per metre."
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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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`(200 dollars)/(300m) = (? dollars)/(1m)` ; Solve for the "?" amount of dollars.
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Method 1) "Cross-factor multiply" :
Note: Given: "
`(a)/(b) = (c)/(d) ; [b\\eq 0; d\\eq 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 =
`(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:
" [
`(2)/(3)` dollar] per metre."
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Method 2) Note:
\frac{200 dollars}{300m} = \frac{? dollars}{1m} ;

⇔ = "
`(200)/(300)`
`(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. "
`((2)/(3) dollars)/(metre)` " or;
`\frac{0.67 dollars} {m}` ; or: $0.67 / metre .

⇒ {since: "
`(2)/(3)` of 1 dollar" = " \frac{2}{3} dollars of 100 cents" ;
⇒ {since: "1 dollar = 100 cents"} ;

⇒ {and: "
`(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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