QuestionEmma just moved into a new apartment and finds out she has two different options for internet.
- Company A charges per month with a non-refundable installation fee.
- Company B offers a comparable internet package and charges per month with a non-refundable installation fee.
a) Write an equation for the total cost to get the internet from Company for months.
b) Which sentence below, BEST describes the meaning of the slope of the equation above.
Select an answer
c) Which line on the graph below represents the cost to rent from Company A for months?
The Select an answer line represents the cost to get the internet from Company A for months.
d) If Emma is planning on staying in the apartment for one semester of school ( 4 months), which internet plan should she choose. Which answer below best explains using a comparison?
Select an answer
e) If Emma is unsure how many months she needs to have internet, help her know under what conditions she should choose each of the plans.
Company is always best, because it started out cheaper.
Company is always best, becasue it costs less per month.
In order to make a decision, Emma should look at the break even point! Company is best for the first month, and Company is best after that.
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Studdy Solution
STEP 1
1. Company A charges a monthly fee and a one-time installation fee.
2. Company B charges a different monthly fee and a different one-time installation fee.
3. We need to write an equation for the total cost for Company A and analyze the cost comparison between the two companies over time.
STEP 2
1. Write the equation for the total cost from Company A.
2. Interpret the meaning of the slope in the equation.
3. Identify the correct line on a graph representing Company A's cost.
4. Compare costs for a specific duration (4 months).
5. Determine conditions under which each plan is preferable.
STEP 3
To write the equation for the total cost from Company A for months, we consider both the monthly charge and the installation fee.
The total cost for Company A is given by:
STEP 4
The slope of the equation represents the monthly charge from Company A, which is per month.
STEP 5
To determine which line on a graph represents the cost from Company A, we look for the line with a slope of 220 and a y-intercept of 100.
The line with these characteristics represents the cost to get the internet from Company A for months.
STEP 6
To compare costs for 4 months, calculate the total cost for each company:
- Company A:
- Company B:
Company B is cheaper for 4 months.
STEP 7
To determine under what conditions each plan is preferable, calculate the break-even point:
Set the costs equal:
Solve for :
Company A is cheaper for less than approximately 1.43 months, and Company B is cheaper after that.
The answers are:
a)
b) The slope represents the monthly charge from Company A.
c) The line with a slope of 220 and y-intercept of 100 represents Company A.
d) For 4 months, Company B is cheaper.
e) Company B is better after approximately 1.43 months.
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