For an international telephone call, a telephone company charges $0.43 for the first minute, $0.32 for each additional minute, and a $2.10 service charge. If the cost of a call is $5.73, how long did the person talk?

Verified step by step guidance

1. Start by setting up an equation to represent the total cost of the call. Let \( x \) be the number of additional minutes talked. The equation will be: \( 0.43 + 0.32x + 2.10 = 5.73 \).
2. Subtract the service charge and the cost of the first minute from the total cost: \( 5.73 - 2.10 - 0.43 = 0.32x \).
3. Simplify the left side of the equation to find the total cost of the additional minutes: \( 3.20 = 0.32x \).
4. Solve for \( x \) by dividing both sides of the equation by 0.32: \( x = \frac{3.20}{0.32} \).
5. The total talk time is the first minute plus the additional minutes: \( 1 + x \).

Key Concepts

Cost Structure

Understanding the cost structure is essential for solving this problem. The total cost of the call includes a fixed service charge and variable charges based on the duration of the call. In this case, the service charge is $2.10, and the cost per minute varies: $0.43 for the first minute and $0.32 for each additional minute.

Algebraic Equations

To find the duration of the call, we need to set up an algebraic equation based on the given costs. The total cost can be expressed as the sum of the service charge and the charges for the minutes talked. This requires translating the problem into an equation that can be solved for the unknown variable, which in this case is the number of minutes.

Solving for Variables

Once the equation is established, solving for the variable involves isolating it on one side of the equation. This may include combining like terms and performing arithmetic operations. Understanding how to manipulate equations is crucial for determining how long the person talked based on the total cost of the call.