Problem 36 - Algebra and Trigonometry

Question

The rate for a particular international person-to-person telephone call is \(\$ 0.43\) 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?

Step-by-Step Solution

Answer

The person talked for 10 minutes.

Step 1: Conversion of Verbal Statements into an Equation

From the problem, the total cost of the call is made up by the three parts. The equation that represents this is given as: \(\$2.10 (service charge) + $0.43 (first minute call rate) + $0.32(n - 1: additional minute's rate) = $5.73\). This equation accounts for everything including the first minute, the additional minutes (with the deduction of the first minute: hence \(n - 1\)) and the service charge. Here n stands for the total duration of the call.

Step 2: Simplify the Equation

Combine similar terms to simplify the equation to the form ax + b = c, where 'a', 'b', and 'c' are constants. Move all the constant terms to the right side of the equation. \[0.32n = 5.73 - 2.10 - 0.43\] \[0.32n = 3.20\]

Step 3: Solve for the Unknown

Now solve for 'n'. We do this by dividing both sides of the equation by 0.32. \(n = \frac{3.20}{0.32} = 10\). So, the unknown, 'n', which stands for the total duration of the call is 10 minutes. The person talked for 10 minutes.