Concept explainers
Renting versus buying a photocopier A certain office can purchase a photocopier for $5800 with a maintenance fee of $25 a month. On the other hand, they can rent the photocopier for $95 a month (including maintenance). If they purchase a photocopier, each copy would cost 3¢; if they rent, the copy is 6¢ per copy. The office estimates that they make 8000 copies a month.
(a) Find a formula for the cost
(b) Find a formula for the cost
(c) Make a table of the cost of each method for 1 year to 6 years of use, in 1-year increments.
(d) After how many moths of use would the cost be the same for each method?
(a)
To Find:
A formula for the cost of purchasing a photocopier for n months.
Answer to Problem 1P
Solution:
Explanation of Solution
The cost of the photocopier is $5800.
The maintenance cost per month is $25.
When the photocopier is purchased, the cost per copy is 3¢.
The office makes 8000 copies per month.
Then, the cost of 8000 copies is
Because, $1=100¢.
We need to find a formula for purchasing and using the photocopier for
The total cost for purchasing and using a photocopier can be obtained by adding the cost of photocopier, maintenance cost and the cost of the copies.
Therefore,
Hence, the formula for purchasing and using a photocopier is
(b)
To Find:
A formula for the cost of renting a photocopier.
Answer to Problem 1P
Solution:
Explanation of Solution
The cost for rent and maintenance of the photocopier per month is $95.
When the office rent a photocopier, the cost per copy is 6¢.
The office makes 8000 copies per month.
Then, the cost of 8000 copies is
We need to find a formula for renting and using the photocopier for
Therefore,
Hence, the formula for purchasing and using a photocopier is
(c)
To Find:
A table for the cost of each methods.
Answer to Problem 1P
Solution:
n | Purchase (in dollars) |
Rent (in dollars) |
12 | 8980 | 6900 |
24 | 12160 | 13800 |
36 | 15340 | 20700 |
48 | 18520 | 27600 |
60 | 21700 | 34500 |
72 | 24880 | 41400 |
Explanation of Solution
The formula for purchasing and using a photocopier is
Substitute
Then,
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Then,
Substitute
Then,
Substitute
Then,
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Then,
Substitute
Then,
The formula for renting and using a photocopier is
Substitute
Then,
Substitute
Then,
Substitute
Then,
Substitute
Then,
Substitute
Then,
Substitute
Then,
(d)
To Find:
A formula for the cost of renting a photocopier.
Answer to Problem 1P
Solution:
After 19 months the cost is same for each method.
Explanation of Solution
The formula for purchasing and using a photocopier is
The formula for renting and using a photocopier is
It is given that the cost becomes same for both the methods.
Therefore,
Now,
Then,
Hence,
Hence, after 19 months the cost is same for each method.
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Chapter P Solutions
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