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. Find the cost of making 40 copies.

Answer 1

Hint: For the first 40 copies, calculate the first 10 copies at the rate of Rs. 1.50 and the rest at the rate of Rs. 1.00. Now calculate the values and find their sum to get the answer.

Complete step-by-step answer:
It is given in the question that a photocopy store charges Rs. 1.50 per copy for the first 10 copies and Rs. 1.00 per copy after the $10^{th}$ copy. It is given that, if x is the number of copies, and y is the total cost of photocopying, then we have to find the cost of making 40 copies. Now as the question has asked us to assume x as the number of copies and y as the total cost of photocopying, we will first try to construct a function of x and y and then later substitute to find the required values.
We will first see the value of y in terms of x for various ranges of x, such as for the first 10 values of x varying from $0< x$ less than or equal to 10. The value of y will be 1.5x as it is mentioned that the rate for first 10 copies is Rs. 1.50 per copy. Now for the remaining copies, after removing 10 copies from x copies, we get (x - 10) copies. We will apply the rate of Rs.1.00 for all the copies after the 10th copy. So, for $x > 10$, the function of y will be, $\left( 1.5\times 10 \right)+\left( 1 \right)\left( x-10 \right)=15+x-10=\left( 5+x \right)$. Hence, we can write it as,
$y=\left\{ \begin{align}
  & Rs.1.5x,0< x\le 10 \\
 & Rs.\left( 5+x \right), x >10 \\
\end{align} \right\}$.
Now, we have been asked to find the value of y in rupees if x is 40,
So, the cost for 10 copies will be $10\times 1.5=Rs.15$.
After the first 10 copies, only 30 are left. So, the cost for the next 30 will be $30\times 1=Rs.30$.
Therefore, the cost of making 40 copies is Rs. $15$ + Rs. $30$ = Rs. $45.$

Note: One can also solve this question by another method too. Here we have already formed the function of y in terms of x as we know that for $x> 10$, $y= x+5$ where x is the number of copies, On putting the value of x we can get the answer.