Question

Beak mobile charges $40a month plus a one time fee of $50 Horizon charges $30 a month plus a one time fee of $100
Let x represent the number of months and y represent the cost
Write the equation that represents the cost of Beak mobile
Write the equation that represents the cost of Horizon mobile
In how many months do the cell phone plans cost the same
What is the solution to this system write it in ordered pairs
The solution means that at month ___ the cost of the cell phone plans are both ____

Answer 1

To create the equations for the two mobile plans:

1. **Beak Mobile Cost Equation**:
Beak Mobile charges $40 a month plus a one-time fee of $50. The equation can be written as:
\[
y = 40x + 50
\]

2. **Horizon Mobile Cost Equation**:
Horizon charges $30 a month plus a one-time fee of $100. The equation can be written as:
\[
y = 30x + 100
\]

Next, to find out how many months it takes for both plans to cost the same, we need to set the two equations equal to each other and solve for \(x\):
\[
40x + 50 = 30x + 100
\]

Subtract \(30x\) from both sides:
\[
10x + 50 = 100
\]

Subtract \(50\) from both sides:
\[
10x = 50
\]

Now, divide by \(10\):
\[
x = 5
\]

Now we can plug \(x = 5\) into either equation to find the cost at this point. Using the Beak Mobile equation:
\[
y = 40(5) + 50 = 200 + 50 = 250
\]

Thus, the solution to the system is the ordered pair \( (5, 250) \).

Therefore, the answer to your statements would be:
- The solution means that at month **5**, the cost of the cell phone plans are both **$250**.