Questions: A student missed 16 problems on a biology test and received a grade of 66%. If all the problems were of equal value, how many problems were on the test? Follow the problem-solving process and round your answer to the nearest integer.

Solution Steps

To find the total number of problems on the test, we can use the information given about the percentage score and the number of problems missed. The student received a 66% score, which means they got 66% of the problems correct. If they missed 16 problems, we can set up an equation where the total number of problems minus the number of problems missed equals 66% of the total number of problems. Solving this equation will give us the total number of problems.

Let \( x \) be the total number of problems on the test. The student missed 16 problems, so the number of problems answered correctly is \( x - 16 \). Given that the student scored 66%, we can express this as: \[ \frac{x - 16}{x} = 0.66 \]

To eliminate the fraction, we can multiply both sides by \( x \): \[ x - 16 = 0.66x \] Rearranging gives: \[ x - 0.66x = 16 \] This simplifies to: \[ 0.34x = 16 \]

Now, we can solve for \( x \) by dividing both sides by 0.34: \[ x = \frac{16}{0.34} \approx 47.0588 \] Rounding to the nearest integer, we find: \[ x = 47 \]

Final Answer