Question

Arnold is shopping around for a new cell phone provider. He is considering two different plans. Plan 1 has a monthly fee of $18.50 plus $0.15 per minute. Plan 2 costs $27 per month with unlimited minutes of talk. Find the number of minutes Arnold would have to talk to have the same cost under both plans.

a) 50 minutes
b) 56.7 minutes
c) 45.5 minutes
d) 60.3 minutes

Answer 1

Arnold would have to talk for 56.7 minutes for both phone plans to cost the same. This is found by setting the cost equation for Plan 1 equal to the flat fee of Plan 2 and solving for the number of minutes.

Step-by-step explanation:

To determine when Arnold would have the same cost under both cell phone plans, we need to set up an equation where the cost of Plan 1 equals the cost of Plan 2. For Plan 1, the cost is the monthly fee plus the per-minute charge, which is represented as $18.50 + $0.15x, where x is the number of minutes. For Plan 2, the cost is a flat monthly fee of $27. Thus, we have the equation $18.50 + $0.15x = $27.

Next, to solve for x, we subtract $18.50 from both sides of the equation:

• $18.50 + $0.15x - $18.50 = $27 - $18.50
• $0.15x = $8.50

Now, we divide both sides by $0.15 to find the number of minutes:

• x = $8.50 / $0.15
• x = 56.7 minutes

So, Arnold would have to talk for 56.7 minutes to have the same cost under both plans. The closest answer choice to this calculation is answer b) 56.7 minutes.

Answer 2

Arnold would need to talk for approximately 56.7 minutes for the costs under both plans to be equal. Option B is the answer.

Step-by-step explanation:

To find the number of minutes for equal costs under both plans, we set up the cost expressions. Plan 1 has a monthly fee of $18.50 plus an additional $0.15 per minute. Plan 2 costs a fixed $27 per month with unlimited minutes. Setting the two costs equal to each other and solving

for the number of minutes (x):

18.50 + 0.15x = 27

Solving for x:

0.15x = 8.50

x = 8.50 / 0.15 ≈ 56.7 minutes

Thus, Arnold would need to talk for approximately 56.7 minutes for the costs under both plans to be the same.

Option B is the answer.