A high school has designed he yearbook. A company charges $900 to assemble the master copy and $42 to make additional copies. The total selling price depends on how many copies are made. Write a funtion rule and determine how much will the school save on each book by ordering 600 instead of 200?

Question

A high school has designed he yearbook. A company charges $900 to assemble the master copy and $42 to make additional copies. The total selling price depends on how many copies are made. Write a funtion rule and determine how much will the school save on each book by ordering 600 instead of 200?

Answer 1

looks like

Cost = 900 + 42n , where n is the number of books

for 600 books cost = 900+42(600)
= 26100
cost per book = 26100/600 = 43.50

for 200 books cost = 900 + 200(42)
= 9300
cost per book = 9300/200 = 46.50

so how much do they save per book?

Answer 2

To determine the function rule for the total selling price, we can break it down into two parts: the cost for assembling the master copy and the cost for making additional copies.

Let's denote the number of copies made as "x."

The cost for assembling the master copy is a fixed cost of $900. This cost does not depend on the number of copies made.

The cost for making additional copies is multiplied by the number of additional copies beyond the master copy. Since the question states that each additional copy costs $42, we can represent this part of the cost as 42(x-1), where (x-1) represents the additional number of copies beyond the master copy.

Thus, the function rule for the total selling price can be written as:
Total Selling Price = Cost for Assembling the Master Copy + Cost for Making Additional Copies
= $900 + 42(x-1)
= $900 + 42x - 42

Now, to determine how much the school will save on each book by ordering 600 instead of 200, we need to calculate the difference in total selling price for these two quantities.

For 200 copies:
Total Selling Price1 = $900 + 42(200-1) = $900 + 42(199) = $900 + $8378 = $9278

For 600 copies:
Total Selling Price2 = $900 + 42(600-1) = $900 + 42(599) = $900 + $25158 = $26058

To find the savings, we subtract the total selling price of 200 copies from the total selling price of 600 copies:
Savings = Total Selling Price2 - Total Selling Price1
= $26058 - $9278
= $16780

Therefore, the school will save $16,780 on each book by ordering 600 copies instead of 200 copies.