Math  /  Algebra

QuestionEmma just moved into a new apartment and finds out she has two different options for internet. - Company A charges $220\$ 220 per month with a non-refundable $100\$ 100 installation fee. - Company B offers a comparable internet package and charges $150\$ 150 per month with a non-refundable $200\$ 200 installation fee. a) Write an equation for the total cost to get the internet from Company AA for tt months. y=y= 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 tt months?
The \square Select an answer \checkmark line represents the cost to get the internet from Company A for tt 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 AA is always best, because it started out cheaper. Company BB is always best, becasue it costs less per month. In order to make a decision, Emma should look at the break even point! Company AA is best for the first month, and Company BB is best after that. Question Help: Message instructor
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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 t t months, we consider both the monthly charge and the installation fee.
The total cost y y for Company A is given by: y=220t+100 y = 220t + 100

STEP 4

The slope of the equation y=220t+100 y = 220t + 100 represents the monthly charge from Company A, which is $220 \$220 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 t t months.

STEP 6

To compare costs for 4 months, calculate the total cost for each company:
- Company A: y=220(4)+100=880+100=980 y = 220(4) + 100 = 880 + 100 = 980 - Company B: y=150(4)+200=600+200=800 y = 150(4) + 200 = 600 + 200 = 800
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: 220t+100=150t+200 220t + 100 = 150t + 200
Solve for t t : 220t150t=200100 220t - 150t = 200 - 100 70t=100 70t = 100 t=100701.43 t = \frac{100}{70} \approx 1.43
Company A is cheaper for less than approximately 1.43 months, and Company B is cheaper after that.
The answers are: a) y=220t+100 y = 220t + 100 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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