Question

Englebert wants to buy a new car, and has narrowed his choices down to 2 possibilities. The first possibility is a hybrid that gets 100 miles per gallon gas mileage, but costs $35,000. The second possibility is a sedan that gets 25 miles a gallon but only costs $20,000. Englebert is going to pay cash for either car. He drives 25,000 miles a year, in an area where the gas price is $4.00 a gallon.


•For both the hybrid and sedan cases, write linear equations that show what Englebert's cost of ownership is versus the years he owns the cars. Work collectively with your classmates on this pr

Answer 1

do you know how to solve systems of linear equations?

Answer 2

Not that much.......still learning......can you give example.....would help.....not looking for just answer....but help...

Answer 3

OK. Well let's take the first car. It gets 100 miles per gallon. He drives 25,000 miles a year. So how many gallons does he use in a year?

Answer 4

2500000

Answer 5

That would be right if the car needed 100 gallons of gas to go one mile. But it is the opposite: it goes 100 miles with 1 gallon of gas.

Answer 6

ooohhhh ok 1000

Answer 7

how do you get 1000?

Answer 8

1000 is not correct

Answer 9

help

Answer 10

If you can go 100 miles with one gallon, how many miles can you go with two gallons?

Answer 11

200

Answer 12

And how many miles with 3 gallons?

Answer 13

300

Answer 14

OK ... so if you want to go 500 miles, how many gallons do you need?

Answer 15

5

Answer 16

and if you want to go 5,000 miles, how many gallons?

Answer 17

1000

Answer 18

why 1000?

Answer 19

no

Answer 20

the relationship is that if we have X number of gallons, we can go 100x miles.

Answer 21

50

Answer 22

And similarly, if we want to go Y miles, we need Y/100 gallons. right?

Answer 23

So how many gallons if we want to go 25,000 miles?

Answer 24

(50 was right, for 5,000 miles!)

Answer 25

250

Answer 26

perfect!!! OK, so we know in 1 year he uses 250 gallons of gas. And gas costs $4 per gallon. so how much money does he spend on gas in a year?

Answer 27

1000

Answer 28

yes! And that's in one year, so if he drives the car for, say, "Y" years, how much does he spend on gas?

Answer 29

what is Y

Answer 30

the number of years he drives the car

Answer 31

So your answer can have the "Y" in it

Answer 32

ok sorry for being so difficult....

Answer 33

So it would be C=

Answer 34

the cost of the car plus the yearly price of gas, both added together

Answer 35

C=gc + miles
C=1000+35,000
C=45,000

Answer 36

well gas isn't 1000 total, it's 1000 per year, so 45000 is only correct if he were driving for one year. But the question asked you for an equation of the total cost versus number of years. If he's driving for Y years, then the cost of the hbyrid is

C= 35,000 + 1000Y

Now, you can do the same thing for the other car, too

Answer 37

•How many years will it take for the gas savings with the hybrid to make up for the larger purchase price of the hybrid?

Answer 38

First you have to find the equation for the other car.

Answer 39

ok so the other car would be
C=
one moment

Answer 40

confused

Answer 41

I know to divide 25,000 miles by 25 miles a gallon.....then what?

Answer 42

that tells you how many gallons he uses. multiply that by cost per gallon.

Answer 43

that's all per year, remember

Answer 44

40000

Answer 45

4000......sorry

Answer 46

per year, right? so what's the equation for the total cost as a function of Y, the number of years?

Answer 47

yes

Answer 48

so what's the equation for the total cost as a function of Y, the number of years?

Answer 49

C=25,000 +4000Y
or
C=25,000+1000Y

Answer 50

very very close - remember the two cars cost different amounts

Answer 51

you got the hard part which is the cost of gass per year, but you didn't get the initial price of the car

Answer 52

C=20,000 +4000Y

Answer 53

right, and what about the other one?

Answer 54

C=35,000 +1000Y

Answer 55

yes!

Answer 56

•How many years will it take for the gas savings with the hybrid to make up for the larger purchase price of the hybrid

Answer 57

they're asking how many years does it take before the total cost of the two cars are equal. so set the two equations equal to each other and solve for Y.

Answer 58

? Help plzzzz...you are so helpful

Answer 59

35,000 +1000Y = 20,000 +4000Y

Answer 60

So I need to get the Y's isolated

Answer 61

exactamundo

Answer 62

right

Answer 63

35,000+1000Y=20,000+4000Y
-40000Y -4000Y

35,000+3000Y=20,000Y
-

Answer 64

So far am I right?

Answer 65

You are on the right track but got the sign wrong on the left side. 1000 minus 4000 isn't +3000.

Answer 66

It's probably easier to move the 1000Y instead of moving the 4000Y (but, the answer will come out the same no matter which way you choose)

Answer 67

30,000Y=20,000............so lost right now....

Answer 68

35,000+1000Y=20,000+4000Y

Subtract 1000Y from both sides.
Then subtract 20,000 from both sides.
What do you get?

Answer 69

35,000Y=23,000Y

Answer 70

no, let's do it step by step. First let's subtract 1000Y.

35,000 + 1000Y = 20,000 + 4000Y
- 1000Y - 1000Y

What do you get?

Answer 71

35,000y =23,000Y
I have problems with my negative and positive

Answer 72

You're mixing up the terms that have Y and the terms that do not have Y. If you're subtracting a Y term you ignore the terms that don't have Ys.

Answer 73

100 + 35Y - 35Y is just equal to 100.

Answer 74

ok

Answer 75

So what's 35,000 + 1000Y - 1000Y?