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# a rental car company has a linear pricing plan

## Tags: Mathematik

21:13 Uhr, 22.11.2022

Tag!
Would like to hear any tips about how to solve the first question.

a rental company has a linear pricing plan. the total cost, $C\phantom{\rule{0.12em}{0ex}},$ to rent a car for $2,4,6,10$ days,d, is shown
what is the daily rate for the pricing plan?

Für alle, die mir helfen möchten (automatisch von OnlineMathe generiert):
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21:34 Uhr, 22.11.2022

Hello,

it seems that the cost function is as follows: $C\phantom{\rule{0.12em}{0ex}}=r\phantom{\rule{0.12em}{0ex}}\cdot d\phantom{\rule{0.12em}{0ex}}+f\phantom{\rule{0.12em}{0ex}}$, where $C\phantom{\rule{0.12em}{0ex}}$=total cost, $r\phantom{\rule{0.12em}{0ex}}$=daily rate, $d\phantom{\rule{0.12em}{0ex}}$=number of days, $f\phantom{\rule{0.12em}{0ex}}$=fixed rate

Now you can set up two equations with two of the value pairs. I take the first two: $\left(2/105\right),\left(4/195\right)$

$105=r\phantom{\rule{0.12em}{0ex}}\cdot 2+f\phantom{\rule{0.12em}{0ex}}$

$195=r\phantom{\rule{0.12em}{0ex}}\cdot 4+f\phantom{\rule{0.12em}{0ex}}$

Now you can calculate the value of $r\phantom{\rule{0.12em}{0ex}}$ and $f\phantom{\rule{0.12em}{0ex}}$. Start by subtracting the first equation from the second equation.

Advice: Make a check with the value pair $3$ or $4$.

greetings,
pivot

23:03 Uhr, 22.11.2022

check this pivot and pls tell me if you find it correct

195−105=r(4)+f−(r(2)+f)
$2r\phantom{\rule{0.12em}{0ex}}=90$
$r\phantom{\rule{0.12em}{0ex}}=45$

the daily rate is $45$ dollars

an equation that could represent this would be
$C\phantom{\rule{0.12em}{0ex}}=45\left(d\phantom{\rule{0.12em}{0ex}}\right)+f\phantom{\rule{0.12em}{0ex}}$
Cost is equal to the daily rate times the number of days of the rental plus the fixed rate.

23:41 Uhr, 22.11.2022

That's right. Now you can use $105=r\phantom{\rule{0.12em}{0ex}}\cdot 2+f\phantom{\rule{0.12em}{0ex}}$ to determine the value of $f\phantom{\rule{0.12em}{0ex}}$.

06:49 Uhr, 23.11.2022

or this way:

$C\phantom{\rule{0.12em}{0ex}}\left(x\phantom{\rule{0.12em}{0ex}}\right)=r\phantom{\rule{0.12em}{0ex}}\cdot x\phantom{\rule{0.12em}{0ex}}+f\phantom{\rule{0.12em}{0ex}}$

$C\phantom{\rule{0.12em}{0ex}}\left(2\right)=105$
$C\phantom{\rule{0.12em}{0ex}}\left(4\right)=195$

$2r\phantom{\rule{0.12em}{0ex}}+f\phantom{\rule{0.12em}{0ex}}=105$
$f\phantom{\rule{0.12em}{0ex}}=105-2r\phantom{\rule{0.12em}{0ex}}$

$4r\phantom{\rule{0.12em}{0ex}}+f\phantom{\rule{0.12em}{0ex}}=195$
$4r\phantom{\rule{0.12em}{0ex}}+\left(105-2r\phantom{\rule{0.12em}{0ex}}\right)=195$
$2r\phantom{\rule{0.12em}{0ex}}=90$
$r\phantom{\rule{0.12em}{0ex}}=45$
$f\phantom{\rule{0.12em}{0ex}}=15$

$C\phantom{\rule{0.12em}{0ex}}\left(x\phantom{\rule{0.12em}{0ex}}\right)=45x\phantom{\rule{0.12em}{0ex}}+15$

18:07 Uhr, 23.11.2022

that is great / toll!. Thanks!

18:07 Uhr, 23.11.2022

that is great / toll!. Thanks!

18:18 Uhr, 23.11.2022

You're welcome.