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A telephone company charges $x$ cents for the first minute of a call and charges for any additional time at the rate of $y$ cents per minute. If a certain call costs $5.55$ and lasts more than 1 minute, which of the following expressions represents the length of that call, in minutes?

$
  A.\dfrac{{555 - x}}{y} \\
  B.\dfrac{{555 + x - y}}{y} \\
  C.\dfrac{{555 - x - y}}{y} \\
  D.\dfrac{{555}}{{x + y}} \\
 $

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Last updated date: 17th Jun 2024
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Answer
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Hint:In this question, we represent the function in an algebraic form. This can be done by representing the function by any variable.
Since $x$ and $y$ are in cents, then we have to convert $5.55$ in cents as well.
Let assume the total time of the call be ‘t’ in minutes and make the equation by using the given terms in the question.

Complete step by step solution:
Let us assume that the call lasts for ‘t’ minutes.
And to convert dollars into cents, we need to multiply it by 100.

$
  {\text{As}},{\text{ }}\$ 1 = 100{\text{ }}cents \\
  \$ 5.55 = 5.55 \times 100 \\
   = 555{\text{ }}cents \\
 $

Then, the cost for the first minute = $x$ cents
Cost for the remaining call = $y(t - 1)$ cents
Hence, the total cost of the call = $x + y(t - 1){\text{ cents - - - - (i)}}$ cents
According to the question, the cost of the call is \[\$ 5.55 = 555{\text{ cents - - - - (ii)}}\] so,
On equating equation (i) and (ii) we get,
Cost of the call = Cost for the first minute + cost for the remaining call
$
  555 = x + y(t - 1) \ldots \left( {{\text{in cents}}} \right) \\
  x + yt - y = 555 \\
  yt - y = 555 - x \\
  yt = 555 - x + y \\
  t = \dfrac{{555 - x + y}}{y} \\
 $

So,option (C) is correct

Note: The first thing we should keep in mind is that all the terms of an equation must have the same units. Students must solve these types of questions carefully. The major mistake students usually make is that there are (t-1) additional minutes which do not cost the same as it cost for the first minute, so do the calculations carefully. And also remember to use the terms with the same units by changing them.