I have to do ten math problems for homework. I've done the rest but I am totally stumped on these two. If someone could not only do them for me but PLEASE PLEASE explain how to do it (show work), would be much appreciated. I need to not only have these answers, but understand it as well.
Best answer is the reward. Thank you.
4.) A truck can be rented from Basic Rental for $50 per day. In addition, you have to pay $0.20 per mile. Continental charges $20 per day in addition to $0.50 per mile to rent out the same truck. How many miles must you drive in a day to make the rental cost for Basic Rental a better deal than that for continental?
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10.) You need to choose between two telephone plans for local calls. Plan A charges $25 per month for unlimited calls. Plan B charges a monthly fee of $13 with a charge of $0.06 per local call. How man local telephone calls in a month make Plan A the better deal? As you can see, they are both similar, which is why I'm stumped. I know you have to use x and y but I can't do it. Plus, the way the question is worded, they don't just want the answer, then need to know how much better it is etc. let "x" represent the # of miles you drive in a day...
Therefore, the cost of using Basic Rental for 1 day can be represented by the expression...
Basic Rental Cost = $50 + $0.20x
and the cost of using Continental for 1 day can be represented by the expression...
Continental Cost = $20 + $0.50x
You want to find the break point... so you want to set the two expression equal to each other...
Basic Rental Cost = Continental Cost
$50 + $0.20x = $20 + $0.50x.... and solve for "x"
$30 = $0.30x
x = 100 miles...
Now to determine whether the miles have to be less than 100 miles (x<100) or greater than 100 miles (x>100)...
pick x = 99 and x = 101 to see which one will have the better deal...
So when x = 99...
BC = $50 + $0.20x = $50 + $0.20(99) = $50 +19.8 = $69.8
CC = $20 + $0.50x = $20 + $0.50(99) = $20 + $49.5 = $69.5...
BC is MORE EXPENSIVE when x < 100...
Therefore you will get a better deal with Basic if you drove MORE THAN 100 miles...
PROBLEM 10:
figure out the number of call in one month...
you know that Plan A charges $25 per month and you have unlimited calling... so... Plan A = $25
you know that Plan B can be represent by the expression...
Plan B = $13 + $0.06x.... where x represents # of local calls
now set that expression equal to $25 dollars to find the breaking point...
Plan A = Plan B
$25 = $13 + $0.06x
$12 = $0.06x
x = 200 local calls....
Therefore plan Ais the better deal as long as the number of calls exceeds 200 calls.... for #4 you can use a simple linreg equation. Y=m(x)+b
if you have a graphing calculator. input these 2 equations.
Y= .20(x) + 50 and Y=.50(x) + 20
and where these two lines intersect is your answer. #4
Write them out as two separate equations.
Let y = total cost
x = miles driven
For basic rental, call that y1
y1 = 50 + 0.20x
There is a 50 flat payment so that is your y-intercept.
For Continental, call that y2
y2 = 20 + 0.50x
You can see that if you're going short distances, continental will be cheaper. If you're traveling far, basic will be cheaper.
Set the two equations equal to one another to find out at what mileage they are equal.
20 + 0.50x = 50 + 0.20x
solve for x
0.30x = 30
x = 100
If you drive 100 miles, both car companies will charge the same amount.
Because Continental has a smaller y-intercept, it will be cheaper all the way up until 100 miles. Because it has a larger slope, it will be more expensive after 100 miles. For Basic rental to be a better deal you'd have to drive over 100 miles.
#10
This is very similar, like you said.
Let y = phone charges
Plan A is a flat rate, so it is
y1 = 25
Plan B is
y2 = 13 + 0.06x
Like above, set them equal
13 +0.06x = 25
0.06x = 12
x = 200
So unless you make over 200 calls a month, Plan B is the better deal.
With these types of problems your main plan is to find two equations, and set them equal to one another to find our where they are equal.
Any more q's on this, please ask. Note: You do not two seperate equations, nor do you need Y in the equation. Just put one company on one side of the equation and the other on the other side.
Set up the equation with Basic Rental on the left side and Continental on the right. x represents miles. Make BR<C because we want to find when it is a lower value. Also 50 and 20 are used as constants, respectively.
.20x+50<.50x+20
30<.30x
100<x
A: When the mileage is greater than 100, BR is the better deal.
Same thing, put A on the left and B on the right, because we want A to be less set it up as A<B. x represents minutes. Also 25 and 13 are used as constants, respectively.
25<.06x+13
12<.06x
200<x
A: When more than 200 minutes are used, plan A is the better deal. 4.) 50+0.20x=20+0.50x
Then you solve for x. Once you get that answer that will let you know when they will be equal, add one to it and Basic Rental will be better.
10.)25=13+0.06x
Then solve for x. That will let you know when the plans will be equal and add one to get when Plan A is better.
I didn't want to just give you the answers, but if you still need help then you can e-mail me. |
