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Chapter 10: Problem 5

Home heating oil is sold by the gallon. Last winter, the Romano family used 370 gallons of oil at a price of \(\$ 3.91\) per gallon. If the price increases 9\(\%\) next year, what will their approximate heating expense be? Round to the nearest ten dollars.

Short Answer

Expert verified
Based on the calculations, the approximate heating expense for the Romano family next year, rounding to the nearest ten dollars, is \(\$1590\)

Step by step solution

01

Calculate Initial Spending

First, calculate the total spending of the Romano family based on last winter's consumption and price per gallon. This can be done by multiplying the gallons of oil consumed (370 gallons) with the price per gallon (\$3.91). This yields the initial spending in dollars. The calculation is as follows: \(370 * 3.91\).
02

Calculate Increase

The next step is to calculate the amount of price increase for next year. It's given that the price will increase by 9%. This means that the total spending will also increase by 9%. To calculate the increase, multiply the initial spending with 9% (or 0.09). The calculation is as follows: \(Initial Spending * 0.09\).
03

Calculate Total Expense

Finally, calculate the total heating expense for next year by adding the calculated price increase to the initial spending. The formula for this calculation is: \(Initial Spending + Price Increase\)
04

Round off the Final Value

Lastly, round off the final calculated value to the nearest ten dollars. This can be done by dividing the final value by 10, rounding to the nearest whole number, and then multiplying back by 10.

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Key Concepts

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

Understanding Percentage Increase
When we talk about percentage increase, we're figuring out how much something will cost after a price goes up by a certain percent. In our exercise, the Romano family's heating cost will rise by 9%. Here's how you calculate it clearly:
  • First, find the initial cost. Multiply the number of gallons (370) by the price per gallon (\(\$3.91\)). This gives the original spending.
  • Next, calculate the increase by multiplying the initial cost by 0.09 (which represents 9%).
This method helps determine how much more you will pay compared to the original cost. Percentage increases are used everywhere from shopping to budgeting, so understanding this concept is very useful!
Mastering Cost Calculation
Cost calculations are a practical and everyday part of financial mathematics. Let's break down the steps from the exercise:
  • Calculate Initial Cost: Multiply the gallons used by the cost per gallon. Here, that's 370 gallons * \(\$3.91\).
  • Find the Increase: Apply the percentage increase (9%) to the initial cost. Multiply the initial spending by 0.09.
  • Total New Cost: Add this increase to the original cost to get the total expense for next year.
This process is crucial in planning budgets or estimating future expenses. Once you understand these steps, you can easily predict and plan for changes in costs over time!
Rounding Numbers Made Simple
Rounding numbers simplifies calculations and makes figures easier to understand, especially in budgeting and financial reports. In this exercise, the final step is to round the calculated expense to the nearest ten dollars.
  • Divide and Round: Take the final calculated value, divide by 10, and round to the nearest whole number.
  • Multiply Back: Multiply this number by 10 to get the rounded total.
Rounding helps in creating estimates that are easy to comprehend and communicate. It鈥檚 a handy tool, whether you're balancing a checkbook or planning future expenses!

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