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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)
) 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 $

1 answer

Let's address each question one at a time.

  1. Write the equation that represents the cost of Beak-Mobile:

The cost of Beak-Mobile is given by a monthly fee of $40 and a one-time fee of $50. Thus, the equation can be written as: \[ y = 40x + 50 \]

  1. Write the equation that represents the cost of Horizon Phones:

The cost of Horizon Phones is given by a monthly fee of $30 and a one-time fee of $100. Thus, the equation can be written as: \[ y = 30x + 100 \]

  1. In how many months do the two cell phone plans cost the same?

To find when the two plans cost the same, we set the two equations equal to each other: \[ 40x + 50 = 30x + 100 \]

Now, we solve for \( x \): \[ 40x - 30x = 100 - 50 \] \[ 10x = 50 \] \[ x = 5 \]

So, the two plans cost the same after 5 months.

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

To find the cost at \( x = 5 \), we can substitute \( x \) back into either equation. Using the Beak-Mobile equation: \[ y = 40(5) + 50 = 200 + 50 = 250 \]

Thus, the ordered pair solution is: \[ (5, 250) \]

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

The solution means that at month 5, the cost of the cell phone plans are both $250.