A rental car agency charges a flat fee of $110.00 plus $46.00 per day to rent a certain car. Another agency charges a fee of $70.00 plus $54.00 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.

9
3
5
8

Question

A rental car agency charges a flat fee of $110.00 plus $46.00 per day to rent a certain car. Another agency charges a fee of $70.00 plus $54.00 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.

9
3
5
8

anonymous · Answer

@CalebBeavers

anonymous · Answer

Give me a second

anonymous · Answer

Do you have a graphing calculator? I dont, but i know how to solve it algebraically

anonymous · Answer

no i don't

anonymous · Answer

Alright well we'll do do it the algebraic way. the first agency's cost can be written as c=46d+110 an the second as c=54d+70. Do you see how i got that? c represents cost and d represents days

anonymous · Answer

ok

anonymous · Answer

Understand how i got those two?

anonymous · Answer

yes

anonymous · Answer

Alright now we can solve the two linear equations,

c=46d+110
c=54d+70

Move the variables to one side:
c-46d=110
c-54d=70

Now how would you solve that?

anonymous · Answer

ok so I subtract both of them

anonymous · Answer

or add

anonymous · Answer

c-46d=110
c-54d=70
------------
c-100=180

anonymous · Answer

this is what you're doing:
adding these two together:
c-46d=110 
c-54d=70

but first you have to cancel out one of the variables so that you only have one to solve for. so how would we cancel out c?

anonymous · Answer

What would you mutiply the top equation by so that the c turns into -c?

anonymous · Answer

subtract c from both equations

anonymous · Answer

Focus on the top one for now, we need c to turn into -c so that when we add the c from the bottom one, it will equal 0 and we will just have d to solve for. 

so to do that we multiply the whole top equation by -1

anonymous · Answer

When we do that itll give us 

-c+46d=-110
c-54d=70 

now when we add the equations together, the c will cancel out and well just have one variable that we can solve for

anonymous · Answer

So now add the equations together

anonymous · Answer

100 = -220

anonymous · Answer

Where did the d go? 

46d+(-54d)=-8d and -110+70=-40 so were left with:

-8d=-40

anonymous · Answer

Now solve for d and that is your answer

anonymous · Answer

oopps sorry forgot so then I will divide -8 from boths sides

anonymous · Answer

the answer would be 5

anonymous · Answer

Thats correct

anonymous · Answer

Thank you so much!!!! could you help me with another question?

anonymous · Answer

I could try, post it as a new one