A rental car agency charges a flat fee of $124.00 plus $45.00 per day to rent a certain car. Another agency charges a fee of $36.00 plus $56.00 per day to rent the same car.

Using a graphing calculator, find the number of days for which the costs are the same. Round your answer to the nearest whole day.

x=quantity of days

$38.00+$2.75x=$31.75+$4.00x

We can cancel all $ ...

38.00+2.75x=31.75+4.00x

It is just as important to cancel symbols as numbers.

Next, we isolate x.

We will begin by subtracting 31.75 from both sides ...

-31.75+38.00+2.75x=4.00x

6.25+2.75x=4.00x

Then, we will divide both sides by 4.00 ...

(6.25/4.00) + ((2.75x) / 4.00) = (4.00x) / 4.00

1.56+0.69x=x

Then, we will subtract 0.69x from both sides ...

-0.69x+1.56+0.69x=x-0.69x

1.56=0.31x

Then, we will divide both sides by 0.31 ...

1.56/0.31 = (0.31x) / 0.31

5=x

Let's check our numbers ...

The original equation was ...

$38.00+$2.75x=$31.75+$4.00x

38.00+2.75 (5) = 31.75+4.00 (5)

38.00+13.75=31.75+20.00

51.75=51.75