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Question

Question

You are planning on signing for a cell phone plan.

Beak-Mobile is charging $40 a month with an additional one-time fee of $50

Horizon Phones is charging $30 a month with an additional one-time fee of $100

Let x represent the number of months and let y represent the cost

(1 point)
1) Write the equation that represents the cost of Beak-Mobile

2) Write the equation that represents the cost of Horizon Phones

3) In how many months do the two cell phone plans cost the same?

4) What is the solution to this system of equations? Write this as an ordered pair.

5) The solution means that at month 
, the cost of the cell phone plans are both $

GPT-4o mini · Answer

To solve the problem, let's break it down step by step.

Equation for Beak-Mobile:
The cost of Beak-Mobile can be represented by the equation:
\[ y = 40x + 50 \]
Here, $ y $ is the total cost, $ 40x $ is the monthly cost for $ x $ months, and $ 50 $ is the one-time fee.
Equation for Horizon Phones:
The cost of Horizon Phones can be represented by the equation:
\[ y = 30x + 100 \]
Here, $ 30x $ is the monthly cost for $ x $ months, and $ 100 $ is the one-time fee.
Finding When Costs are Equal:
To find out when the two plans cost the same, we set the two equations equal to each other:
\[ 40x + 50 = 30x + 100 \]
Now, solve for $ x $:
\[ 40x - 30x = 100 - 50 \]
\[ 10x = 50 \]
\[ x = 5 \]
So, the two plans cost the same after 5 months.
Finding the Solution as an Ordered Pair:
Now we can find the cost at $ x = 5 $ by substituting it into either cost equation (let's use Beak-Mobile):
\[ y = 40(5) + 50 = 200 + 50 = 250 \]
Therefore, the solution as an ordered pair is:
\[ (5, 250) \]
Interpreting the Solution:
The solution means that at month 5, the cost of the cell phone plans are both $250.

In summary: