Question

The number of traffic accidents in our city has dropped by \(17 \%\) this year. If last year's total was 475 , what is this year's total? A. 281 B. 394 C. 400 D. 600

Short answer

394

Step-by-step solution

Calculate the decrease in accidents

To find how many fewer accidents occurred this year, multiply last year’s total by the decrease percentage. The decrease is given by: \[ \text{Decrease} = 475 \times \frac{17}{100} \] Calculate the value of this expression.

Perform the calculation

Perform the multiplication to find the number of accidents decreased:\[ 475 \times 0.17 = 80.75 \] So, there were 80.75 fewer accidents this year.

Subtract the decrease from last year's total

Subtract the calculated decrease from last year’s total to find this year’s total number of accidents:\[ 475 - 80.75 = 394.25 \] Since the number of accidents must be a whole number, we round to 394.

Choose the correct multiple-choice answer

Compare the calculated number with the given options: A. 281 B. 394 C. 400 D. 600 The closest match is option B.

Key concepts

mathematical reasoning

Mathematical reasoning involves understanding and applying mathematical concepts to solve problems. In our exercise, we first identify the total number of accidents from last year, which is 475. With a given percentage decrease of 17%, we determine how this affects the total. We use the concept of percentage to figure out the exact decrease. This demands critical thinking and the ability to break down complex problems into manageable steps. By calculating the decrease and subtracting it from the original figure, we can logically determine the solution. Mathematical reasoning, therefore, helps us methodically tackle the problem.

GED test prep

Preparing for the GED exam involves practicing a variety of mathematical problems, including those involving percentages. This type of problem is common in the GED test. Knowing how to handle percentage decreases can save time and increase accuracy. First, you need to convert the percentage into its decimal form by dividing by 100. Next, multiply this decimal by the original number to find the decrease. Then, subtract this result from the original number. Understanding these steps can boost your confidence and help you perform better on the test.

Consistent practice with such problems can significantly improve your test scores. Remember, the more you practice, the more familiar these types of questions become.

arithmetic operations

This problem involves basic arithmetic operations: multiplication and subtraction. With percentages, converting the percentage to a decimal is crucial. Here’s how:

• Convert 17% to a decimal: 17% equals 0.17 when divided by 100.
• Multiply: Multiply this decimal by the original number, 475, to find the decrease: 475 × 0.17 = 80.75.
• Subtract: To find the new total, subtract this decrease from the original number: 475 - 80.75.

Following these steps ensures accuracy. Working through each step carefully can help you understand the arithmetic involved and improve your problem-solving skills in related scenarios.

real-world math problems

Understanding percentages and how to calculate them is a valuable real-world math skill. It helps in various daily activities, like reading sale prices, calculating discounts, or understanding statistics.

In this exercise, we apply percentage decrease to a practical example - traffic accidents. This approach can be used in other real-world problems.

• Identify the original amount: In this case, 475 traffic accidents.
• Determine the percentage change: A 17% decrease.
• Calculate the decrease: Multiply the original amount by the decimal form of the percentage.
• Find the new amount: Subtract the calculated decrease from the original amount.

These steps can be applied to various contexts, making percentage decrease calculations a versatile and essential math skill.