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Chapter 10: Problem 15

The Waldner family paid their electric bill using balanced billing all last year. The monthly payment was \(m x\) dollars. At the end of the year, the electric company told them they had a credit of \(c x\) dollars due to over payment. This meant they paid for more electricity than they used. Express the value of the electricity used by the Waldners last year algebraically.

Short Answer

Expert verified
The value of the electricity used by the Waldners last year is represented algebraically as \(12m x - c x\).

Step by step solution

01

Understand the payments

The Waldners have paid their electric bill using balanced billing with a monthly payment of \(m x\) dollars for a year. This means the total amount paid in a year is \(12 \times m x\) dollars.
02

Understand the overpayment

At the end of the year, the electric company told them they had a credit of \(c x\) dollars due to overpayment. This overpayment will be subtracted from the total amount they paid in order to calculate the actual cost of electricity they used.
03

Calculate the cost

To calculate the cost of electricity used by the Waldners, subtract the overpayment from the total amount paid. Algebraically this can be represented as \(12m x - c x\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Balanced Billing
Balanced billing is a convenient method to handle household utility bills, like those for electricity. Instead of paying variable amounts each month鈥攕ometimes higher in summer or winter due to air conditioning or heating鈥攗sers pay a set fee monthly.
This method helps families budget their expenses more evenly throughout the year.
For the Waldner family, this meant their monthly payment was expressed as \(m x\) dollars.
  • This approach simplifies financial planning since the amount paid isn't dependent on actual usage each month.
  • By the end of the year, if the family pays more than they use, it's termed an overpayment, resulting in a credit.
Using balanced billing requires an estimate of the expected annual usage. The total amount paid is calculated as the monthly payment times 12, covering the entire year.
Overpayment
Overpayment occurs when more money is paid than the actual cost of electricity used.
For the Waldner family, this was highlighted by the electric company reporting a credit of \(c x\) dollars at year-end.
This means they've essentially loaned money to the utility company, which they can use to offset future bills.
  • An overpayment means the pre-set balanced billing rate was higher than their actual usage.
  • This can result from reduced electricity consumption or overestimation of expected use when the balanced plan was set up.
On a positive note, overpaying means they won't have immediate worries about upcoming bills鈥攁s they have credits to use next year.
Electric Bill Calculation
Calculating the actual electricity cost involves some algebraic understanding. Given the Waldners' monthly payment was \(m x\), they paid a total of \(12m x\) dollars for the year.
However, since they overpaid by \(c x\) dollars, the calculation of the true value becomes: \[\text{Actual Cost} = 12m x - c x\]This formula spells out that to find what they truly owed, the overpayment credit must be subtracted from the total paid.
  • It鈥檚 essential to know both the total paid amount and the overpayment credit to accurately determine the cost.
  • This method uses algebra to simplify what might otherwise be a complex assortment of monthly bills.
Applying this approach ensures a clear understanding of what you truly owe, separating it from the seemingly fixed monthly billing rate.

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