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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?
Choose 1 answer:
(A) 4
(B) 19
(c) 86
(D) 105

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? $\newline$ Choose $1$ answer: $\newline$ (A) $4$ $\newline$ (B) $19$ $\newline$ (C) $86$ $\newline$ (D) $105$

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Mean, median, mode, and range: find the missing number

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?

\newline

Choose

1

answer:

\newline

(A)

4

\newline

(B)

19

\newline

(C)

86

\newline

(D)

105

Find Total Number: First, we need to find the total number of problems on the test. We can do this by using the percentage of problems the student answered correctly. $\newline$ We have: $\newline$ Percentage of problems answered correctly = $81.9\%$ $\newline$ Number of problems answered correctly = $86$ $\newline$ To find the total number of problems, we use the formula: $\newline$ Total number of problems = Number of problems answered correctly / (Percentage of problems answered correctly / $100$ )
Calculate Total: Now we calculate the total number of problems: $\newline$ Total number of problems = $86 / (81.9 / 100)$ $\newline$ Total number of problems = $86 / 0.819$ $\newline$ Total number of problems $\approx 105$ (rounded to the nearest whole number since the number of problems cannot be a fraction) $\newline$ We have found the total number of problems on the test.
Find Incorrectly Answered: Next, we need to find the number of problems the student answered incorrectly. We can do this by subtracting the number of problems answered correctly from the total number of problems. $\newline$ Number of problems answered incorrectly $=$ Total number of problems $-$ Number of problems answered correctly
Calculate Incorrectly Answered: Now we calculate the number of problems answered incorrectly: $\newline$ Number of problems answered incorrectly = $105 - 86$ $\newline$ Number of problems answered incorrectly = $19$

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