Question
The phone company A Fee and Fee has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 230 minutes, the monthly cost will be $116.5. If the customer uses 520 minutes, the monthly cost will be $218.
A) Find an equation in the form y=mx+b, where x is the number of monthly minutes used and y is the total monthly of the A Fee and Fee plan.
Answer: y=
Do not use any commas in your answer.
B) Use your equation to find the total monthly cost if 1000 minutes are used.
Answer: If 1000 minutes are used, the total cost will be
dollars
A) Find an equation in the form y=mx+b, where x is the number of monthly minutes used and y is the total monthly of the A Fee and Fee plan.
Answer: y=
Do not use any commas in your answer.
B) Use your equation to find the total monthly cost if 1000 minutes are used.
Answer: If 1000 minutes are used, the total cost will be
dollars
Answers
GPT-4o mini
Let's start by extracting the necessary information to find the equation.
We know that:
1. When \( x = 230 \) minutes, \( y = 116.5 \).
2. When \( x = 520 \) minutes, \( y = 218 \).
We can represent the monthly cost as a linear equation in the form \( y = mx + b \), where:
- \( m \) is the cost per minute,
- \( b \) is the flat monthly fee.
**A)** First, we’ll find \( m \) (the cost per minute) and \( b \) (the flat fee) using the two points we've been given.
From the points \( (230, 116.5) \) and \( (520, 218) \), we can set up the following equations:
1. \( 116.5 = m(230) + b \) (Equation 1)
2. \( 218 = m(520) + b \) (Equation 2)
Next, we can subtract Equation 1 from Equation 2 to eliminate \( b \):
\[
218 - 116.5 = m(520) - m(230)
\]
This simplifies to:
\[
101.5 = m(290)
\]
Now we solve for \( m \):
\[
m = \frac{101.5}{290} \approx 0.350
\]
Now that we have \( m \), we can substitute it back into either Equation 1 or Equation 2 to find \( b \). Using Equation 1:
\[
116.5 = 0.350(230) + b
\]
\[
116.5 = 80.5 + b
\]
\[
b = 116.5 - 80.5 = 36
\]
Thus, the equation is:
\[
y = 0.350x + 36
\]
**Final Answer for A:**
\[ y = 0.350x + 36 \]
---
**B)** Now we can use the found equation to calculate the total monthly cost if 1000 minutes are used.
Substituting \( x = 1000 \) into the equation:
\[
y = 0.350(1000) + 36
\]
\[
y = 350 + 36
\]
\[
y = 386
\]
Thus, if 1000 minutes are used, the total cost will be:
**Final Answer for B:**
The total cost will be 386 dollars.
We know that:
1. When \( x = 230 \) minutes, \( y = 116.5 \).
2. When \( x = 520 \) minutes, \( y = 218 \).
We can represent the monthly cost as a linear equation in the form \( y = mx + b \), where:
- \( m \) is the cost per minute,
- \( b \) is the flat monthly fee.
**A)** First, we’ll find \( m \) (the cost per minute) and \( b \) (the flat fee) using the two points we've been given.
From the points \( (230, 116.5) \) and \( (520, 218) \), we can set up the following equations:
1. \( 116.5 = m(230) + b \) (Equation 1)
2. \( 218 = m(520) + b \) (Equation 2)
Next, we can subtract Equation 1 from Equation 2 to eliminate \( b \):
\[
218 - 116.5 = m(520) - m(230)
\]
This simplifies to:
\[
101.5 = m(290)
\]
Now we solve for \( m \):
\[
m = \frac{101.5}{290} \approx 0.350
\]
Now that we have \( m \), we can substitute it back into either Equation 1 or Equation 2 to find \( b \). Using Equation 1:
\[
116.5 = 0.350(230) + b
\]
\[
116.5 = 80.5 + b
\]
\[
b = 116.5 - 80.5 = 36
\]
Thus, the equation is:
\[
y = 0.350x + 36
\]
**Final Answer for A:**
\[ y = 0.350x + 36 \]
---
**B)** Now we can use the found equation to calculate the total monthly cost if 1000 minutes are used.
Substituting \( x = 1000 \) into the equation:
\[
y = 0.350(1000) + 36
\]
\[
y = 350 + 36
\]
\[
y = 386
\]
Thus, if 1000 minutes are used, the total cost will be:
**Final Answer for B:**
The total cost will be 386 dollars.