Question

A photocopy store charges Rs 1.50 per copy for the first 10 copies and Rs 1.00 per copy after the 10th copy. Let x be the number of copies, and let y be the total cost of photocopying.
(i) Draw a graph of the cost as x goes from 0 to 50 copies.
(ii) Find the cost of making 40 copies.

Answer 1

Hint: In this question, it is very important to make the equation for solving this question. As it is given in this question, we have to take x as the number of copies and y as the total cost of photocopying. We can either solve the (ii) part either by using the equation or the graph as both methods are equally good and both would provide the same answer.

Complete step-by-step answer:
As mentioned in the question, we have to draw the graph and then we have to find the cost of making 40 copies.
Now, as it is given in the question that x is the number of copies and y as the total cost of photocopying, we can make the equation as follows
\[\begin{align}
  & \Rightarrow y=1.50\times 10+1\times (x-10) \\
 & \Rightarrow y=15+(x-10) \\
 & \Rightarrow y=x+5 \\
\end{align}\]
For plotting this line, we can first find three points on this line and then we can plot these points on the graph to get the equation on line as follows
Three points that lie on the given line are
For x=0,
\[\begin{align}
  & \Rightarrow y=x+5 \\
 & \Rightarrow y=+5 \\
 & \Rightarrow y=5 \\
\end{align}\]
A- (0, 5)
 For x=1,
\[\begin{align}
  & \Rightarrow y=x+5 \\
 & \Rightarrow y=1+5 \\
 & \Rightarrow y=6 \\
\end{align}\]
B- (1, 6)
 For x=-1,
\[\begin{align}
  & \Rightarrow y=x+5 \\
 & \Rightarrow y=-1+5 \\
 & \Rightarrow y=4 \\
\end{align}\]
C- (-1, 4)
Hence, the plot is as follows

(ii) And we can see from the graph that for x=40 which means that when the total number of copies is 40, we can get the total cost as 45 as follows
\[\begin{align}
  & \Rightarrow y=x+5 \\
 & \Rightarrow y=40+5 \\
 & \Rightarrow y=45 \\
\end{align}\]

Note: Another way of getting the cost of printing 40 copies is by checking the y component or the ordinate of the point where abscissa is 40, we can see that there the ordinate comes out to be as 45. Also, it is very important to carefully plot the points and hence the graph of the equation of the line as by making a single mistake, one could never get to the correct answer.