Question

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. $\frac{555-x}{y}$
• B. $\frac{555+x-y}{y}$
• C. $\frac{555-x+y}{y}$
• D. $\frac{555-x-y}{y}$
• E. $\frac{555}{x+y}$

Answer 1

The correct option is A $\frac{555-x}{y}$

Given that

Cost that the company charges for the first minute of a call $=$ $x$ cents

Cost for additional time of a call per minute $=$ $y$ cents

If a call costs 5.55$andlastsmorethan$1$ minute,

To find the length of the call in minutes

Let ${}^{\prime }{l}^{\prime }$ be the number of minutes the call lasted.

We know that

1=100$ cents

Cost of the call $=$ 5.55$

$=$ $555$ cents

From above, as the call exceeded $1$ minute,

Cost of the call $=$ Cost of the call for the first minute $+$ cost of the call for the $l$ minutes

$555$ $=$ $x$ $+$ $(l$ $\times$ $y)$

Rearranging the terms, we get

$(l$ $\times$ $y)$ $=$ $555$ $-$ $x$

$l$ $=$ $\frac{555-x}{y}$

Therefore, Length of that call in minutes is ${}^{\prime }$$\frac{555-x}{y}$${}^{\prime }$.