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Owen answered a set of math and history Quiz Bowl questions. Owen correctly answered
72% of all the 200 questions. However, Owen answered
53.3% of the math questions correctly. If
45% of the questions were in math, what percent of history questions did Owen answer correctly?
(Round to the nearest percent. Ignore the
% symbol when entering your answer. For example, if the answer is
11.2%, enter 11.)

Owen answered a set of math and history Quiz Bowl questions. Owen correctly answered $72 \%$ of all the $200$ questions. However, Owen answered $53.3 \%$ of the math questions correctly. If $45 \%$ of the questions were in math, what percent of history questions did Owen answer correctly? $\newline$ (Round to the nearest percent. Ignore the $\%$ symbol when entering your answer. For example, if the answer is $11.2 \%$ , enter $11$ .)

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Find what percent one number is of another: word problems

Full solution

Q. Owen answered a set of math and history Quiz Bowl questions. Owen correctly answered

72 \%

of all the

200

questions. However, Owen answered

53.3 \%

of the math questions correctly. If

45 \%

of the questions were in math, what percent of history questions did Owen answer correctly?

\newline

(Round to the nearest percent. Ignore the

\%

symbol when entering your answer. For example, if the answer is

11.2 \%

, enter

11

.)

Calculate Correct Answers: Step $1$ : Calculate the total number of questions Owen answered correctly. $\newline$ Owen correctly answered $72\%$ of all $200$ questions. $\newline$ Correctly answered questions = $72\%$ of $200$ $\newline$ = $0.72 \times 200$ $\newline$ = $144$
Total Math Questions: Step $2$ : Calculate the total number of math questions. $\newline$ $45$ \% of the questions were in math. $\newline$ Math questions = $45\%$ of $200$ $\newline$ = $0.45 \times 200$ $\newline$ = $90$
Math Questions Correct: Step $3$ : Calculate the number of math questions Owen answered correctly. $\newline$ Owen answered $53.3\%$ of the math questions correctly. $\newline$ Correctly answered math questions = $53.3\%$ of $90$ $\newline$ = $0.533 \times 90$ $\newline$ = $47.97$ $\newline$ Since the number of questions Owen can answer correctly must be a whole number, we round to the nearest whole number. $\newline$ Correctly answered math questions $\approx 48$
Total History Questions: Step $4$ : Calculate the total number of history questions. $\newline$ Total questions = $200$ $\newline$ Math questions = $90$ $\newline$ History questions = Total questions - Math questions $\newline$ = $200 - 90$ $\newline$ = $110$
History Questions Correct: Step $5$ : Calculate the number of history questions Owen answered correctly. $\newline$ Total correctly answered questions = $144$ $\newline$ Correctly answered math questions = $48$ $\newline$ Correctly answered history questions = Total correctly answered questions - Correctly answered math questions $\newline$ = $144 - 48$ $\newline$ = $96$
Percentage of Correct Answers: Step $6$ : Calculate the percentage of history questions Owen answered correctly. $\newline$ Percentage of correctly answered history questions $= \frac{\text{Correctly answered history questions}}{\text{Total history questions}} \times 100$ $\newline$ $= \frac{96}{110} \times 100$ $\newline$ $= 0.8727272727272727 \times 100$ $\newline$ $= 87.27272727272727$ $\newline$ Rounded to the nearest percent: $87\%$

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