Question

Fastbet is charging)59 a month with an additional one time fee of $75. Speedconnect is charging $35 a month with an additional one time fee of $120 Let x represent the number of months and y the cost

Answer 1

Write the solution to this system of equations in ordered pair

Answer 2

To represent the costs of Fastbet and Speedconnect using the variables \(x\) (number of months) and \(y\) (total cost), we can create equations based on their pricing structures.

1. **Cost Calculation for Fastbet**
- Monthly cost: $59
- One-time fee: $75
- Therefore, the equation for Fastbet is:
\[
y = 59x + 75
\]

2. **Cost Calculation for Speedconnect**
- Monthly cost: $35
- One-time fee: $120
- Therefore, the equation for Speedconnect is:
\[
y = 35x + 120
\]

Now, we can analyze these equations further or find out when the costs are equal or compare them over a given range of months.

### To find when the costs are equal:
Set the two equations equal to find the number of months \(x\) where the costs are the same:

\[
59x + 75 = 35x + 120
\]

### Solve for \(x\):
1. Subtract \(35x\) from both sides:
\[
59x - 35x + 75 = 120
\]
\[
24x + 75 = 120
\]

2. Subtract 75 from both sides:
\[
24x = 45
\]

3. Divide both sides by 24:
\[
x = \frac{45}{24} \approx 1.875
\]

### Interpretation:
At approximately 1.875 months, the costs of Fastbet and Speedconnect are equal.

You can also plug that value back into either equation to find the cost \(y\) at that point, if desired.

If you need any further analysis or comparisons, feel free to ask!

Answer 3

To find the ordered pair solution to the system of equations representing the costs of Fastbet and Speedconnect, we found that the two equations are set equal to each other:

1. **Fastbet:**
\[
y = 59x + 75
\]

2. **Speedconnect:**
\[
y = 35x + 120
\]

We found that the two costs are equal when \(x \approx 1.875\), which we can denote as follows:

1.875 is the number of months. Now, we can substitute \(x \approx 1.875\) back into either equation to find \(y\):

### Substituting into the Fastbet Equation:
\[
y = 59(1.875) + 75
\]
\[
y \approx 110.625 + 75
\]
\[
y \approx 185.625
\]

### Substituting into the Speedconnect Equation:
\[
y = 35(1.875) + 120
\]
\[
y \approx 65.625 + 120
\]
\[
y \approx 185.625
\]

Both methods yield the same result for \(y\).

### Ordered Pair Solution:
Thus, the solution to this system of equations in ordered pair form \((x, y)\) is:
\[
\left( \frac{15}{8}, 185.625 \right) \quad \text{or approximately } (1.875, 185.625)
\]

This means that after approximately 1.875 months, both services cost about $185.63.