Question

A bookseller sold a number of Geography textbooks at the rate of Rs x per book, \[a + 2\] number of history textbooks at the rate of Rs \[x + 2\]per book and \[a - 2\] number of mathematics textbooks at the rate of Rs \[x - 2\] per book. What is his total sale in Rs?
A) \[3x + 3a\]
B) \[3ax + 8\]
C) \[9ax\]
D) \[{x^3}{a^3}\]

Answer 1

Hint: Product of number of items sold by the cost per item is the total sale of that item. Use this method to find the individual sales of each book then add the sale of all the books.

Complete step-by-step solution:
In the question the number of different books sold and their per book prices are given, so we can easily find the sale of each book by taking the product of the number of books sold by price per book.

First, we will multiply the number of geography books sold by the price per book to find sales of Geography textbooks, \[ax\].

Now, we will multiply the number of history books sold by the price per book to find sales of history textbooks, \[\left( {a + 2} \right)\left( {x + 2} \right)\].

Now, we will multiply the number of math books sold by the price per book to find sales of math textbooks, \[\left( {a - 2} \right)\left( {x - 2} \right)\].

Adding all the sales to find the total sale,

\[ax + \left( {a + 2} \right)\left( {x + 2} \right) + \left( {a - 2} \right)\left( {x - 2} \right)\]

As, we get the individual sale of each book so, we will add all the sales to find the total sale,

\[
  ax + a\left( {x + 2} \right) + 2\left( {x + 2} \right) + a\left( {x - 2} \right) + \left( { - 2} \right)\left( {x - 2} \right) \\
   = ax + ax + 2a + 2x + 4 + ax - 2a - 2x + 4 \\
   = 3ax + 8 \\
 \]

Therefore, the sale of all the books is Rs \[3ax + 8\].
Thus, the correct answer is option A.

Note:
To simplify the binomial \[\left( {a + b} \right)\left( {c + d} \right)\], first multiply a with all the terms of second parenthesis and then multiply b with all the terms of second parenthesis.