Dexter took a test and got 5/8 of the questions correct. If he got 60 questions correct, how many questions were there in the test?
Understand the Problem
The question is asking us to determine the total number of questions in a test based on the proportion of questions answered correctly. Dexter answered 5/8 of the total questions correctly, and we know that he got 60 questions correct.
Answer
The total number of questions in the test is $96$.
Answer for screen readers
The total number of questions in the test is $96$.
Steps to Solve
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Identify the total questions based on correct answers Let the total number of questions be $x$. According to the problem, Dexter answered $\frac{5}{8}$ of the total questions correctly. This gives us the equation: $$ \frac{5}{8}x = 60 $$
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Solve for x To find the value of $x$, we can isolate $x$ by multiplying both sides by $\frac{8}{5}$: $$ x = 60 \times \frac{8}{5} $$
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Calculate the total questions Now, we can compute the value: $$ x = 60 \times 1.6 = 96 $$
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Final confirmation of result We verify that 60 is indeed $\frac{5}{8}$ of 96 by checking: $$ \frac{5}{8} \times 96 = 60 $$
The total number of questions in the test is $96$.
More Information
This problem illustrates how fractions can be used to determine unknown quantities. Dexter's performance indicated a clear proportion, allowing us to backtrack to find the full set of questions.
Tips
- Misinterpreting the fraction: It's essential to correctly understand that $\frac{5}{8}$ represents the proportion of questions answered correctly.
- Neglecting to isolate the variable: Be careful to follow algebraic steps to isolate $x$ without making arithmetic errors.
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