Question 1198515: 2) A builder must decide whether to rent or buy an excavating machine. If he were to rent the machine, the rental fee would be €600 per month, and the daily cost (gas, oil, and driver) would be €60 per day it is used. If he were to buy it, his fixed annual cost would be €4,000, and the daily operating and maintenance costs would be €80 per day the machine is used. What is the least number of days each year that he would have to use the machine to justify renting rather than buying it?
Found 2 solutions by proyaop, ikleyn:
Answer by proyaop(69)   (Show Source):
You can put this solution on YOUR website! **1. Define Variables**
* Let 'd' be the number of days the machine is used per year.
**2. Calculate Annual Costs**
* **Renting:**
* Fixed Cost (per year): €600/month * 12 months/year = €7200
* Variable Cost (per year): €60/day * d days = €60d
* Total Cost (Renting): €7200 + €60d
* **Buying:**
* Fixed Cost (per year): €4000
* Variable Cost (per year): €80/day * d days = €80d
* Total Cost (Buying): €4000 + €80d
**3. Set Up the Inequality**
* To justify renting, the total cost of renting must be less than or equal to the total cost of buying:
€7200 + €60d ≤ €4000 + €80d
**4. Solve for 'd'**
* €7200 - €4000 ≤ €80d - €60d
* €3200 ≤ €20d
* d ≥ 160 days
**Therefore, the builder would need to use the machine for at least 160 days each year to justify renting it instead of buying it.**
Answer by ikleyn(52794)  (Show Source):
You can put this solution on YOUR website! .
Eaxctly the same problem (a TWIN, or a duplicate) was solved at this forum
a year or more ago under this link
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1198749.html
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