Victoria took a test and got 80% of the questions right. She answered 20 questions correctly. How many questions were on the test?
The Correct Answer and Explanation is:
To find out how many questions were on Victoria’s test, we start with the information given:
- Victoria got 80% of the questions right.
- She answered 20 questions correctly.
Let x be the total number of questions on the test.
Since 80% of the total number of questions were answered correctly, we can write this as: 0.80×x=200.80 \times x = 20
To solve for x, divide both sides of the equation by 0.80: x=200.80=25x = \frac{20}{0.80} = 25
✅ Final Answer: There were 25 questions on the test.
Explanation (300 words):
Understanding percentages is a fundamental math skill often used in real-life situations. In this problem, Victoria’s test performance is described in terms of a percentage. She got 80% of the questions correct, and we are told that this corresponds to 20 correct answers. The goal is to find the total number of questions on the test.
To solve this, we let x represent the total number of questions. If she got 80% of them right, then mathematically, we express this as: 80% of x=2080\% \text{ of } x = 20
The word “percent” means “per hundred,” so 80% can be written as a decimal: 80%=80100=0.8080\% = \frac{80}{100} = 0.80
Substituting this into the equation, we get: 0.80×x=200.80 \times x = 20
To isolate x, divide both sides of the equation by 0.80: x=200.80=25x = \frac{20}{0.80} = 25
This result tells us that the test had 25 questions in total. To double-check, we calculate 80% of 25: 0.80×25=200.80 \times 25 = 20
Which matches the number of correct answers given in the problem. This confirms our solution is accurate.
This problem is a good example of how algebra can be used to solve real-world percentage problems. Understanding how to translate a word problem into a mathematical equation is key to finding the correct solution.
