Question

The college bookstore sells a textbook that costs $80 for $94 and a textbook that costs $84 for $98.70. If the markup policy of the bookstore is linear, write a linear function that relates sales price S and cost C. What is the cost of a book that sells for $105.75?

Answer 1

Answer:

$90

Explanation:

If the bookstore uses a linear markup policy, a linear relationship can be found between the sales price (S) and cost (C) for every product in the store as follows:

$98.7 - 94 = m(84 - 80)\\m = 1.175\\S-94 = 1.175(C - 80)\\S= 1.175 C$

From that it's easy to see the store works with a simple 17.5% profit margin, so the cost of a book that sells for $105.75 can be found as follows:

$C=\frac{105.75}{1.175} \\C=90$

Answer 2

Answer:

The linear function will be S= 1.175 C

The cost of a book that sells for $105.75 is $90

Explanation:

If the markup policy of the bookstore is linear so we can say that price sale is a constant of the cost

S=x* C   then x=S/C

In the first case,  

x=$94/$80=1.175

In the second case,  

x=$98.70/$84=1.175

So,  if the price of a book is $105.75 ,  the cost will be

C=S/x=  $105.75/1.175=$90