Question

In a recent year, Americans spent about \(\$ 313\) billion dollars on food prepared away from home. Of this total, almost \(48 \%\) was spent on fast food. a. About how much money did Americans spend on fast food? Round your answer to the nearest billion dollars. b. Of the total dollars spent on fast food, about \(64 \%\) was spent on takeout food. About how many fast-food dollars were spent on takeout food?

Short answer

\$150 billion on fast food; \$96 billion on takeout fast food.

Step-by-step solution

Identify Total Spending on Food Away from Home

The problem states that the total amount of money Americans spent on food prepared away from home is \( \$ 313 \) billion.

Calculate Spending on Fast Food

Approximately 48\% of the total spending was on fast food. To find this amount, multiply the total spending by 0.48 (because 48\% as a decimal is 0.48):\[ \$313 \times 0.48 = \$150.24 \] billion. Round this result to the nearest billion dollar: \( \$150 \) billion.

Calculate Spending on Takeout Fast Food

Approximately 64\% of the fast food spending was on takeout food. Multiplying the fast food spending by 0.64 (because 64\% as a decimal is 0.64) will give the amount: \[ \$150 \times 0.64 = \$96 \] billion.

Key concepts

percentage calculations

Understanding percentages is crucial for many real-world problems. A percentage represents a part of a whole and is measured out of 100. In simple terms, percentages help us understand proportions. To convert a percentage to a decimal, divide by 100. For example, 48% becomes 0.48. When you're given a total figure and a percentage, like in our exercise where 48% of American food spending was on fast food, you multiply the total by the decimal form of the percentage: Total Spending on Fast Food = Total Food Spending × Percentage of Fast Food (as a decimal). This step helps us calculate the exact amount spent on fast food. Similarly, when determining how much of the fast food spending was on takeout, you multiply the amount spent on fast food by the takeout percentage.

rounding numbers

Rounding numbers makes them easier to work with and understand. In mathematics, rounding is a way to simplify numbers while keeping them close to the original value. For example, we rounded \[150.24\] billion dollars to \[150\] billion dollars. Here’s a quick way to round numbers:

• Identify which place value you are rounding to (nearest billion, millions, etc.).
• Look at the digit immediately to the right of this place value.
• If it's 5 or more, round up. Otherwise, round down.

This means for 150.24 billion, since the digit immediately to the right of the hundred's place is 2 (which is less than 5), we round down to 150 billion. Rounding helps simplify and communicate results, especially in contexts like financial reports or large data sets.

problem-solving steps

Breaking down a problem into manageable steps can greatly assist in finding a solution. Here's a simple yet effective approach:

• Identify the total and important percentages: Understand what the total value is (e.g., $313 billion) and what percentages are important (48% on fast food and 64% on takeout).
• Convert percentages to decimals: This helps facilitate straightforward multiplication.
• Multiply: Always multiply the total value by the decimal form of the percentage. This gives the specific part or amount in question.
• Round if necessary: Sometimes, particularly in reporting financial data, you may need to round the final number for clarity.

By carefully following these steps, problem-solving becomes systematic and less overwhelming, ensuring that no important parts are overlooked.