Question

The average cost of printing a book in a publishing company is c(x) =, D%7Bx%7D%20" id="TexFormula1" title=" \frac{5.5x+k}{x} " alt=" \frac{5.5x+k}{x} " align="absmiddle" class="latex-formula"> , where x is the number of books printed that day and k is a constant. Find k, if on the day when 200 were printed the average cost was $9 per book.

Answer 1

ANSWER: k = 700

 

WORKINGS

 

Given, c(x) = (5.5x + k)/x where,

c(x) is the average cost of printing a book

x is the number of books printed

k is a constant

 

 

If, c(x) = 9

x = 200

Find k

 

c(x) = (5.5x + k)/x

9 = [5.5(200) + k]/200

 

Multiply both sides of the equation by 200

9 * 200 = [5.5(200) + k]/200 * 200

1800 = 5.5(200) + k

1800 = 1100 + k

 

Subtract 1100 from both sides of the equation

1800 – 1100 = 1100 – 1100 + k

700 = k

k = 700

 

Therefore, given that c(x) = (5.5x + k)/x, if on the day when 200 were printed the average cost was $9 per book, the constant, k = 700

Answer 2

To find K, we must use the fact that
 on the day 200 books were printed
 the average cost was $ 9 per book.
 Thus, substituting the values, we have:
 c (x) = (5.5x + k) / (x)
 9 = (5.5 (200) + k) / (200)
 Clearing K
 (200) * 9 = 5.5 (200) + k
 k = (200) * 9 - 5.5 * (200)
 k = 700
 answer
 the value of the constant k is 700