Alex can purchase a used car for Php 300, 000, which will require him to spend an average of Php 5,000 per month in repairs and maintenance. Or, he can rent a car for Php 30 000 a month, which includes all repairs and maintenance. After how many months will the rented car and purchased car cost the same?
Answers
Answer:
) \begin{gathered} \begin{cases} c_{\text{used}} = 300,000 + 5,000t \\ c_{\text{rented}} = 30,000t \end{cases}\end{gathered}
{
c
used
=300,000+5,000t
c
rented
=30,000t
b) 12 months
Step-by-step explanation:
a) Write a system of equations letting c represent cost in pesos and t represent number of months
For the used car, it involves a single large payment and smaller monthly ones. On the other hand the rented car is paid by the month. Hence,
\begin{gathered} \begin{cases} c_{\text{used}} = 300,000 + 5,000t \\ c_{\text{rented}} = 30,000t \end{cases}\end{gathered}
{
c
used
=300,000+5,000t
c
rented
=30,000t
b) After how many months would the amount spent on each car be the same?
In order to determine that, we equate the two different costs.
\begin{gathered}c_{\text{used}} = c_{\text{rented}}\\300,000 + 5,000t = 30,000t\\300,000 = 25,000t\\12 = t\end{gathered}
c
used
=c
rented
300,000+5,000t=30,000t
300,000=25,000t
12=t
Therefore, it will take 12 months for the cost to be equal.
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