Question
16). A student answered 86 problems on a test correctly and received a grade \( 98 \% \). How many problems were on the test, if all the problems were worth the same number of points?(Round to the nearest whole number)
Ask by Wright Coles. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There were 88 problems on the test.
Solution
Let \( n \) represent the total number of problems on the test.
1. Since the student answered \(86\) problems correctly and received a \(98\%\) score, we have:
\[
\frac{86}{n} \times 100 = 98
\]
2. Dividing both sides by \(100\) gives:
\[
\frac{86}{n} = 0.98
\]
3. Solve for \( n \) by isolating it:
\[
n = \frac{86}{0.98}
\]
4. Calculate the value of \( n \):
\[
n \approx 87.7551
\]
5. Rounding to the nearest whole number:
\[
n = 88
\]
Thus, there were \(88\) problems on the test.
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Beyond the Answer
To find the total number of problems on the test, you can use the formula for percentage. If 86 problems correspond to 98%, you set up the equation: \[ \frac{86}{x} = 0.98 \] Here, \( x \) represents the total number of problems. Rearranging gives you \( x = \frac{86}{0.98} \), which calculates to approximately 87.76. Rounding this to the nearest whole number, the total number of problems on the test is 88. The final answer is that there were 88 problems on the test!