Question

Translate to an equation and solve. Sabrina scored \(90 \%\) on a test with 30 total questions. a. How many questions did she answer correctly? b. What percent did she answer incorrectly? c. How many questions did she answer incorrectly?

Short answer

Answer: Sabrina answered 27 questions correctly and 3 questions incorrectly.

Step-by-step solution

(a) Calculate correct questions

Multiply Sabrina's score (90%, or 0.9 when expressed as a fraction) by the total number of questions (30) to find the number of questions Sabrina answered correctly: 0.9 × 30 = 27.

(b) Calculate incorrect score percentage

Subtract Sabrina's correct score percentage (90%) from 100% to find the percentage of questions she answered incorrectly: 100% - 90% = 10%.

(c) Calculate incorrect questions

Multiply Sabrina's incorrect score percentage (10%, or 0.1 when expressed as a fraction) by the total number of questions (30) to find the number of questions she answered incorrectly: 0.1 × 30 = 3. So, Sabrina answered 27 questions correctly, 10% of the questions were answered incorrectly, and she answered 3 questions incorrectly.

Key concepts

Translating Words to Equations

When solving prealgebra word problems, the first step is often translating the words into mathematical equations. This skill involves reading through the problem carefully, identifying the quantities and operations needed, and then expressing these as mathematical expressions. For example, let's look at Sabrina's test score:

• The phrase "Sabrina scored 90% on a test with 30 total questions" provides us with important numerical information: the percentage (90%) and the total number of questions (30).
• To find out how many questions she answered correctly, we translate "90% of 30 questions" into a mathematical expression: \( 0.9 \times 30 \).

By focusing on the keywords and numerical values in the problem, we can efficiently turn words into equations that help us find a solution.

Percentage Calculations

Understanding percentages is essential in many real-world applications and math activities. Percentages represent how one quantity relates to another as parts of 100. In Sabrina's test scenario, knowing how to work with percentages helps us understand both her success and struggles on the test:

• To calculate the number of questions answered correctly, convert the percentage to a decimal: 90% becomes 0.9. Then multiply by the total number of questions: \( 0.9 \times 30 = 27 \), meaning she answered 27 questions correctly.
• To find the percentage of questions answered incorrectly, subtract her correct percentage from 100%: \( 100\% - 90\% = 10\% \). This means 10% of the questions were answered incorrectly.

Percentage calculations are crucial as they simplify comparing portions and understanding parts of larger wholes.

Solving Equations

The next critical step is solving equations to find unknown values. After translating the problem into equations, we can use these equations to determine our answer. Solving involves straightforward arithmetic operations. Let's see how this applied to the step-by-step solution:

• Once we've determined the percentage for correct responses, we solved for the number of questions: 27.
• We also calculated the percentage of incorrect responses, which was 10%.
• Finally, similar to how we found the correct answers, we solve for how many questions were answered incorrectly by multiplying: \( 0.1 \times 30 = 3 \).

Thus, Sabrina missed 3 questions. Solving equations often involves simple multiplication or subtraction, but having a clear understanding of the relations within the problem is key to reaching a correct solution.