Question

can some one help me
A truck can be rented from company A for $110 a day plus $0.40 per mile. Company b charges $70 a day plus $0.80 per mile to rent the same truck. How many miles must be driven in a day to make the rental cost company a better deal than company B.?

Answer 1

So lets break it down a little. If it's $110 a day, then how much would it be for 2 days? Well since the first day was 110 and the second day was 110 then it must be 220. If you go a third day it's 330. Now you're starting to see the pattern here? The number of days multiplied by the price is the total price.

$110*d=part of the total price

Now see if you can make up another piece to add to that based on the total miles.

Answer 2

When it comes down to it this is an easy question for many people and they have no problems giving you the answer, but if you don't try and work with me while I'm here you'll just fail your tests and not learn anything.

Answer 3

... so from what @Kainui said we can begin to write an equation that represents the total price of company A.

So far we know that each day costs 110.

110 * the number of days = how much we get charged per day

Now we need to add in a term that represents how much we will be charged per mile.

Answer 4

We can do the same thing per mile..

How much is it per mile for company A?

Answer 5

sorry i had to do something this question is not from a test or home work

Answer 6

sweet so your doing it for fun just to learn it?

Answer 7

yes

Answer 8

awesome! I will help you learn how to do this

Answer 9

thank you

Answer 10

Lets reread the first part of the question.

"A truck can be rented from company A for $110 a day plus $0.40 per mile. "

Answer 11

The goal is to write an equation for this sentence

Answer 12

okay

Answer 13

"110 per day plus .40 per mile"

Answer 14

that is the same as:
100 * days + .40 * miles

Answer 15

okay

Answer 16

sry
110 *days + .40 * miles

Answer 17

simplified lets say:
Cost of A = 110 * d + .40 * m

Answer 18

do you follow so far?

Answer 19

yes

Answer 20

great! now it is your turn.

Answer 21

In the same manner write the following as a equation:

Company b charges $70 a day plus $0.80 per mile

Answer 22

B=70*d+70*

Answer 23

close

Answer 24

B=70*d + .8 * m

Answer 25

oh okay

Answer 26

Now looking at both:
A = 110*d + .40*m
B = 70*d + .8 * m

Answer 27

okay

Answer 28

So just looking at it from a logical stand point real quick, A costs more per day but is cheaper per mile and B costs less per day but is more expensive per mile.

Answer 29

yes

Answer 30

If you were going to rent a truck and drive a really long distance which company would you use?

Answer 31

B

Answer 32

but B charges a lot per mile!

Answer 33

for A you have to pay a lot at first... but the miles are really cheap

Answer 34

oh sorry i just saw the question i meant to say a

Answer 35

sweet! so you see where this question is headed

Answer 36

how many miles do I have to drive in order to make it worth it to go with A and not B?

Answer 37

Well first of all the question says it is for 1 day.

So we can set d = 1

Answer 38

Now we have:

A = 110 + .40*m
B = 70 + .8 * m

Answer 39

okay

Answer 40

Would you agree with me that there exists a certain number of miles where if I went with A or B it wouldnt matter because they would cost the same?

Answer 41

yes i agree

Answer 42

Great! So if we drive more than that amount A is the better choice and less then B is the better choice.

Answer 43

Lets find that amount!

Answer 44

To do that we need to solve for the number of miles that makes the total cost the same

Answer 45

okay

Answer 46

A = 110 + .40*m
B = 70 + .8 * m

We want A and B to be equal then we want to solve for m

Answer 47

or:

110 + .40*m = 70+ .8 * m

Answer 48

each of those equations represents the cost and when the cost is equal we have the cool point where it doesnt matter which one we go to

Answer 49

can you solve for m?

110 + .40*m = 70+ .8 * m

Answer 50

okay i have 181.2