SOLUTION: A homeowner must decide whether to buy or rent a garden rototiller. If she rents the machine, the rental fee is $25 per day, and the daily cost to use it is $5 for gas. If she wer

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: A homeowner must decide whether to buy or rent a garden rototiller. If she rents the machine, the rental fee is $25 per day, and the daily cost to use it is $5 for gas. If she wer      Log On

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Question 1109979: A homeowner must decide whether to buy or rent a garden rototiller. If she rents the
machine, the rental fee is $25 per day, and the daily cost to use it is $5 for gas. If she were
to buy the machine, the purchase price is $650, and the daily cost is $7 for gas, oil, and
maintenance. On which day of use would the rental costs become greater than the
ownership costs?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Plot +C+, total cost on vertical axis
Plot +t+ = time in days on the horizontal
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Renting the machine:
(1) +C+=+%28+25+%2B+5+%29%2At+
(2) +C+=+7t+%2B+650+
----------------------------
I'll find out when the costs are equal
+%28+25+%2B+5+%29%2At+=+7t+%2B+650+
+30t+=+7t+%2B+650+
+23t+=+650+
+t+=+28.261+
----------------------
The Rental costs become greater during the 28th day
------------------------------------------------------
check:
I'll say +t+=+28.265+
(1) +C+=+30%2A28.265+
(1) +C+=+847.95+
and
(2) +C+=+7%2A28.265+%2B+650+
(2) +C+=+197.855+%2B+650+
(2) +C+=+847.855+
------------------------------
Ok -the rental costs become slightly higher on day 28