Question

If the United States imports 9.14 billion barrels (bbl) of oil per day, and if this is \(48.2 \%\) of its needs, how much oil is needed per day?

Short answer

The United States needs approximately 18.97 billion barrels of oil per day.

Step-by-step solution

Identify the Percentage of Needs Fulfilled

Understand that the 9.14 billion barrels of oil imported per day accounts for 48.2% of the United States' daily oil needs.

Set up the Proportion

Consider the amount of oil needed as 100% and set up the proportion: 48.2% is to 9.14 billion barrels as 100% is to the total oil needed per day.

Calculate the Total Need

Using the proportion set up in Step 2, calculate the total oil need by dividing the amount of oil imported by the percentage (represented as a decimal) of the needs it fulfills. That is, Total oil needed per day = \(\frac{9.14}{0.482}\).

Perform the Division

Divide 9.14 billion barrels by 0.482 to find the total oil needs per day. Total oil needed per day = \(\frac{9.14}{0.482} \approx 18.96514522821577\) billion barrels.

Key concepts

Proportion Calculations

Proportion calculations are an essential tool in mathematics for comparing ratios and understanding relationships between different quantities. In the context of the exercise, it is used to find the total oil needs of the United States based on the proportion of needs that are fulfilled by imports.

When setting up a proportion, the first step is to determine the ‘part’ and the ‘whole’. In our problem, the ‘part’ is the oil imported, while the ‘whole’ would be the total oil needs. The proportion is expressed as '48.2% is to 9.14 billion barrels as 100% is to x billion barrels', with x representing the amount we seek to find. This creates a cross-multiplication problem, allowing us to solve for x.

To solve a proportion, one can use a simple equation: \( a/b = c/d \), where a, b, c, and d are numbers, and b and d are not zero. We can solve for the unknown by cross-multiplying and then dividing by the known value, which gives us the total oil need per day in the given exercise.

Percentage-to-Decimal Conversion

Converting a percentage to a decimal is a fundamental process in solving percentage problems in mathematics. To convert a percentage to a decimal, one simply needs to divide by 100 or move the decimal point two places to the left.

For example, in our exercise, the percentage given is 48.2%. To convert this number into a decimal for the proportional calculation, we divide 48.2 by 100, which gives us 0.482. This conversion is crucial because percentages cannot be directly used in arithmetic operations such as division or multiplication within the proportion. The decimal form facilitates these operations.

Therefore, when you're tackling a percentage problem, remember this easy step: replace the percent sign with a division by 100, and you're on your way to obtaining a decimal that can be easily used in your calculations.

Word Problems in Algebra

Word problems in algebra involve translating a real-world scenario into a mathematical equation that can be solved using algebraic methods. As seen in our oil import problem, the scenario is presented in a textual format, and the goal is to identify the unknowns and create an equation representing the situation.

The key to solving algebra word problems is to break down the text into manageable parts, identify what is given, and what needs to be found. By determining the relationships between the quantities involved and establishing variables for the unknowns, you can construct an equation that models the problem.

In the context of the oil problem, we are given a percentage and a part of the whole, which leads to setting up a proportion. Understanding how to translate percentages and proportions in the context of word problems is crucial, and practice with various scenarios can help strengthen these critical thinking skills.