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A student answered $86$ problems correctly, which was $81.9\%$ of the total number of problems on the test. How many problems did the student answer incorrectly?

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Percents of numbers: word problems

Full solution

Q. A student answered

86

problems correctly, which was

81.9\%

of the total number of problems on the test. How many problems did the student answer incorrectly?

Determine total number of problems: Determine the total number of problems on the test. $\newline$ We know that $86$ problems represent $81.9\%$ of the total number of problems. To find the total number of problems, we can set up the equation: $\newline$ $86 = 81.9\% \times \text{Total number of problems}$ $\newline$ To solve for the total number of problems, we divide $86$ by $81.9\%$ (or $0.819$ in decimal form). $\newline$ Total number of problems = $\frac{86}{0.819}$
Calculate total number of problems: Calculate the total number of problems. $\newline$ Total number of problems = $\frac{86}{0.819}$ $\newline$ Total number of problems $\approx 105$ (rounded to the nearest whole number since we can't have a fraction of a problem)
Calculate number of incorrect answers: Calculate the number of problems the student answered incorrectly. $\newline$ If the student answered $86$ problems correctly, and there are approximately $105$ problems in total, then the number of incorrect answers is: $\newline$ Number of incorrect answers = Total number of problems - Number of correct answers $\newline$ Number of incorrect answers = $105 - 86$
Evaluate number of incorrect answers: Evaluate the number of incorrect answers. $\newline$ Number of incorrect answers = $105 - 86$ $\newline$ Number of incorrect answers = $19$

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