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Chapter 10: Problem 13

Last year, the Forrester family spent \(\$ 1,882.56\) for electricity. They are opting to use balanced billing for next year. a. What will their monthly payment be under balanced billing? b. Last year, they had their highest bill in the summer, for \(\$ 405.67\) . Their lowest bill was in the winter. Explain why their lowest bill could not be \(\$ 178 .\)

Short Answer

Expert verified
a. Under balanced billing, the Forrester family's monthly payment will be approximately $156.88. b. Their lowest bill can't be $178 as this wouldn't balance out the above-average bills, such as the summer bill of $405.67.

Step by step solution

01

Calculate average monthly electricity bill

To find the average monthly electricity bill for the Forrester family under the balanced billing system, we divide the total bill for the year, \(1882.56\), by the number of months in a year, which is 12. This gives us \(1882.56 / 12 = 156.88\).
02

Examine the possibility of $178 being the lowest monthly bill

Consider the fact that, in order for the average to be around $157, the lows (i.e., costs lower than the average) and the highs (i.e., costs higher than the average) must balance each other. It is known that the highest monthly cost is $405.67 which is approximately $248.79 higher than the average monthly cost. If the lowest monthly bill were as high as $178, there wouldn't be enough 'lows' to balance out that 'high'. Thus, it is impossible for the lowest bill to be $178.

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Key Concepts

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

Understanding Your Average Monthly Electricity Bill
When you're budgeting for household expenses, knowing your average monthly electricity bill is crucial. This figure helps to predict your energy costs and manage your finances better. For the Forrester family, understanding their expenses led them to choose balanced billing, which spreads out their energy costs evenly throughout the year.

To find this average, the total annual cost is divided by 12, the number of months in the year. In their case, dividing the annual electricity bill of \(\$1,882.56\) by 12 months yields \(\$156.88\) per month. This offers a predictable monthly payment, which is especially helpful for families on a tight budget. It smooths out the seasonal spikes from air conditioning in summer or heating in winter that often result in unexpectedly high energy bills.
Strategic Household Budgeting with Balanced Billing
Balanced billing is a strategic tool for effective household budgeting. It allows you to plan your finances better by providing a consistent monthly bill, irrespective of the actual energy consumption for that month.

By opting for balanced billing, the Forrester family avoids the surprise of fluctuating bills. Instead of grappling with a high peak of \(\$405.67\) in the summer and an unknown low in the winter, they can plan their finances around a steady figure of \(\$156.88\) each month. This predictability is key for maintaining a stable household budget.

For many families, such unexpected spikes in utility bills can strain the budget. With balanced billing, it's easier to allocate funds for other necessary expenditures without worrying about fluctuating utility costs.
Applying Financial Algebra to Daily Life
Financial algebra involves using mathematical concepts to solve real-world financial problems. The exercise of determining if \(\$178\) could be the lowest monthly bill under balanced billing is a good example.

We know that an average is found by balancing high and low numbers. With the Forrester's highest bill at \(\$405.67\), significantly above the average of \(\$156.88\), having a 'low' as high as \(\$178\) would not counterbalance the 'high'. In financial algebra, each transaction is seen as an input that affects the overall average.

Through understanding the balance of these inputs, one can make informed decisions about money management. This practical application of mathematical principles helps in everyday budgeting and long-term financial planning.

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Most popular questions from this chapter

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.

The Zwerling family installed central air conditioning in their house this summer. They are compring the electric bills of this summer and last summer. The data is shown. $$\begin{array}{|c|c|c|}\hline \text { Month } & {\text { This Summer }} & {\text { Last Summer }} \\ \hline \text { June } & {\$ 311.20} & {\$ 179.90} \\\ {\text { July }} & {300.65} & {\$ 203.40} \\ {\text { August }} & {302.50} & {\$ 201.11}\end{array}$$ a. What was the total electric bill this summer? b. What was the total electric bill last summer? c. Did the bill increase more or less than 50\(\%\) ?

The Smithtown Water Company uses water meters that measure water usage in gallons. They charge \(\$ 0.12\) per gallon of water. If Jack's previous meter reading was \(45,6621\) gallons and his present water reading is \(46,555\) gallons, what is the amount of his water bill?

Create a year-long budget check-off matrix to chart the following transportation related expenses: Fuel: monthly; Insurance: quarterly; Servicing: every three months; Car wash: bimonthly; Parking: semi- annually; Public transportation: monthly.

A consumer budgets \(480 per month for transportation. She has determined that the cost of a round-trip train ride is \)4 and the cost of each round-trip car ride (factoring in gas, oil, etc.) is \(3. a. Write a budget line equation for this situation. b. Construct the budget line graph that models this situation. c. What do the points on the budget line represent? d. What do points below the budget line represent? e. Suppose that the budgeted amount increases to \)516. Construct the new budget line and the old budget line on the same axes. f. What does the region in between the two lines represent?
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