A high school has designed the yearbook. A company charges $900 to assembly the master copy and $42 to make additional copies. The total selling price depends on how many copies are made. Write a function rule and determine how much will the school save on ecah book by ordering 600 instead of 200?
in algebic expression method... with those two equation..
Total cost=900+42x
totalcostperbook=totalcost/x= 900/x+42
saveoneachbook=costperbook200-costperbook600
= 900/200+42 -900/600 -42
= 900(1/200-1/600)
= 900(400/(200*600))=900 (1/300)= check my work.
32 less than three fourths of a number
To determine the cost savings, we need to calculate the cost per book for both 200 copies and 600 copies. Let's first write the function rule.
Let the number of copies be represented by 'x'.
The cost to assemble the master copy remains constant at $900.
The cost to make additional copies is $42 for each copy.
Therefore, the function rule can be represented as:
Total Cost = $900 + $42 * (x - 1)
To find the cost per book, we divide the total cost by the number of copies:
Cost per Book = Total Cost / number of copies
Now let's calculate the cost per book for 200 copies:
Total Cost for 200 copies = $900 + $42 * (200 - 1) = $900 + $42 * 199 = $900 + $8,358 = $9,258
Cost per Book for 200 copies = $9,258 / 200 = $46.29 per book
Next, let's calculate the cost per book for 600 copies:
Total Cost for 600 copies = $900 + $42 * (600 - 1) = $900 + $42 * 599 = $900 + $25,158 = $26,058
Cost per Book for 600 copies = $26,058 / 600 = $43.43 per book
To determine the cost savings on each book by ordering 600 instead of 200, we subtract the cost per book for 600 copies from the cost per book for 200 copies:
Cost Savings per Book = Cost per Book for 200 copies - Cost per Book for 600 copies
Cost Savings per Book = $46.29 - $43.43 = $2.86
Therefore, the school will save $2.86 on each book by ordering 600 copies instead of 200 copies.