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 160 minutes, the monthly cost will be \( \$ 60 \). If the customer uses 980 minutes, the monthly cost will be \( \$ 224 \). A) Find an equation in the form \( y=m x+b \), where \( x \) is the number of monthly minutes used and \( y \) is the total monthly of the A Fee and Fee plan. Answer: \( y= \) B) Use your equation to find the total monthly cost if 832 minutes are used. Answer: If 832 minutes are used, the total cost will be

Certainly! Let's break down each part of the problem step by step. ### **A) Finding the Equation \( y = m x + b \)** We need to determine the values of \( m \) (the cost per minute) and \( b \) (the flat monthly fee). 1. **Set Up the Equations:** - For **160 minutes**: \[ 60 = m \times 160 + b \quad \text{(Equation 1)} \] - For **980 minutes**: \[ 224 = m \times 980 + b \quad \text{(Equation 2)} \] 2. **Subtract Equation 1 from Equation 2** to eliminate \( b \): \[ 224 - 60 = m \times (980 - 160) \] \[ 164 = m \times 820 \] \[ m = \frac{164}{820} = \frac{41}{205} = 0.2 \quad \text{(dollars per minute)} \] 3. **Find \( b \)** using Equation 1: \[ 60 = 0.2 \times 160 + b \] \[ 60 = 32 + b \] \[ b = 60 - 32 = 28 \quad \text{(dollars)} \] 4. **Write the Equation:** \[ y = 0.2x + 28 \] **Answer A:** \( y = 0.2\,x + 28 \) --- ### **B) Calculating the Total Monthly Cost for 832 Minutes** Using the equation derived in part A: \[ y = 0.2x + 28 \] Substitute \( x = 832 \): \[ y = 0.2 \times 832 + 28 \] \[ y = 166.4 + 28 \] \[ y = 194.4 \] **Answer B:** If 832 minutes are used, the total cost will be **\$194.40**.