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Maths-

General

Easy

Question

In 2016 the total cost for 200 of the books that were sold was between $2,200 and $2,400. Which of the following could be the number of hardcover books that were sold?

A certain book is available from a publishing company in both hardcover and paperback. The table shows the revenue and cost in 2016 for each of the hardcover and paperback books produced by the company.

80
120
160
200

The correct answer is: 80

We use inequalities to solve the problem.
Explanations:
Step 1 of 3:
Let x be the number of hardcover books sold and y be the number of paperback books sold in 2016.
So, we have the equation,
$x plus y equals 200$
$rightwards double arrow y equals 200 minus x$
Step 2 of 3:
The total cost for 200 books that were sold in 2016 was between $2200 and $2400. So, we have the inequality,
$2200 less or equal than 14 x plus 10 y less or equal than 2400$
$rightwards double arrow 2200 less or equal than 14 x plus 10 open parentheses 200 minus x close parentheses less or equal than 2400$
$rightwards double arrow 2200 less or equal than 14 x minus 10 x plus 2000 less or equal than 2400$
$rightwards double arrow 2200 minus 2000 less or equal than 4 x less or equal than 2400 minus 2000$
$rightwards double arrow 200 less or equal than 4 x less or equal than 400$
$rightwards double arrow 50 less or equal than x less or equal than 100$
So, from the above inequality, it is clear that the number of hardcover books sold in 2016 is in between 50 and 100.
Step 3 of 3:
From the given options, only option (A) 80 satisfies the inequality.
Final Answer:
The number of hardcover books that were sold could be — 80.

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