SOLUTION: A mail-order digital photo developer charges 8 cents for each print plus a $2.98 shipping fee. A local developer charges 15 cents for each print. How many digital prints must be or

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Question 227663: A mail-order digital photo developer charges 8 cents for each print plus a $2.98 shipping fee. A local developer charges 15 cents for each print. How many digital prints must be ordered in order that: a. the local developer offers the lower price? b. the mail-order developer offers the lower price?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let P= price in cents for p prints
For mail-order developer:
P%5B1%5D+=+8p+%2B+298
For local developer:
P%5B2%5D+=+15p
When are the prices for p prints equal?
P%5B1%5D+=+P%5B2%5D
8p+%2B+298+=+15p
7p+=+298
p+=+42.6, or 42 prints
For 43 prints, the mail-order developer's price is:
P%5B1%5D+=+8%2A43+%2B+298
P%5B1%5D+=+344+%2B+298
P%5B1%5D+=+642 or $6.42
and the local developer's price is
P%5B2%5D+=+15%2A43
P%5B2%5D+=+645 or $6.45
(b)The mail-order developer's price becomes cheaper at 43 prints
and
For 41 prints:
P%5B1%5D+=+8%2A41+%2B+298
P%5B1%5D+=+328+%2B+298
P%5B1%5D=+626 or, $6.26
and
P%5B2%5D+=+15%2A41
P%5B2%5D+=+615 or, $6.15
(a) The local developer's price remains cheapest up to 41 prints