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A rental car agency charges a flat fee of $38.00 plus $2.75 per day to rent a certain car. Another agency

charges a fee of $31.75 plus $4.00 per day to rent the same car. Use a graphing calculator, find the number of days for which the costs are the same. Round your answer to the nearest whole day.
 
 
Can someone solve this and explain how? 
 
And also these,
 
Solve the system by graphing.
3. {y=-x-9
{3x-y=-11

4. {-0.2x-0.8y=0
{0.7x-0.1y=-2.9

5 {-2x+3y+4=0
{6x-9y=-2



Without graphing, classify each system as independent, dependent, or inconsistent.

{-x-y=-2
{3x-3y=6



{y=2x-7
{4x-2y=14



{8x+2y=0
{y=-4x+2
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3 Answers

Hi Sara;
I can help you with the first question.  Unfortunately, I do not have a graphing calculator.
 
A rental car agency charges a flat fee of $38.00 plus $2.75 per day to rent a certain car. Another agency charges a fee of $31.75 plus $4.00 per day to rent the same car.
 
 
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
 
 
Rental Car Agency Problem
 
let x be the number of days
set up an equation
38+2.75x=31.75+4x (you want the costs to be equal)
38+2.75x-2.75x=31.75+4x-2.75x
38=31.75+1.25x
38-31.75=31.75-31.75+1.25x
6.25=1.25x
625=125x
625/125=x
5=x
answer: 5 days
check your work
38+2.75*5=38+13.75=$ 51.75
31.75+4*5=31.75+20=$ 51.75