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? $\newline$ $21 \%$ $\newline$ (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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Convert between percents, fractions, and decimals: word problems

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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

21 \%

\newline

(Round to the nearest percent. Ignore the

\%

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

11.2 \%

, enter

11

Calculate Owen's Correct Answers: Owen answered $72\%$ of all $200$ questions correctly, so let's find out how many questions that is. $\newline$ $72\%$ of $200$ is $(72/100) \times 200$ .
Calculate Math Questions: Calculating that gives us $(0.72) \times 200 = 144$ questions.
Calculate Correct Math Answers: Now, $45\%$ of the questions were math, which means $55\%$ were history. $\newline$ $45\%$ of $200$ is $(45/100) \times 200$ .
Calculate History Questions: Calculating that gives us $(0.45) \times 200 = 90$ questions in math.
Calculate Correct History Answers: Owen answered $53.3\%$ of the math questions correctly, so let's find out how many math questions he got right. $\newline$ $53.3\%$ of $90$ is $(53.3/100) \times 90$ .
Calculate Percent of Correct History Answers: Calculating that gives us $(0.533) \times 90 = 47.97$ , which we round to $48$ questions.
Calculate Percent of Correct History Answers: Calculating that gives us $(0.533) \times 90 = 47.97$ , which we round to $48$ questions.So, Owen got $48$ math questions right, out of the total $144$ questions he got right. $\newline$ To find out how many history questions he got right, we subtract the math questions from the total correct questions. $\newline$ $144 - 48 = 96$ history questions correct.
Calculate Percent of Correct History Answers: Calculating that gives us $(0.533) \times 90 = 47.97$ , which we round to $48$ questions.So, Owen got $48$ math questions right, out of the total $144$ questions he got right. $\newline$ To find out how many history questions he got right, we subtract the math questions from the total correct questions. $\newline$ $144 - 48 = 96$ history questions correct.Now we need to find out what percent $96$ is of the total history questions. $\newline$ We already calculated that $55\%$ of the questions were history, so $55\%$ of $200$ is $(55/100) \times 200$ .
Calculate Percent of Correct History Answers: Calculating that gives us $(0.533) \times 90 = 47.97$ , which we round to $48$ questions.So, Owen got $48$ math questions right, out of the total $144$ questions he got right. $\newline$ To find out how many history questions he got right, we subtract the math questions from the total correct questions. $\newline$ $144 - 48 = 96$ history questions correct.Now we need to find out what percent $96$ is of the total history questions. $\newline$ We already calculated that $55\%$ of the questions were history, so $55\%$ of $200$ is $(55/100) \times 200$ .Calculating that gives us $48$ $0$ questions in history.
Calculate Percent of Correct History Answers: Calculating that gives us $(0.533) \times 90 = 47.97$ , which we round to $48$ questions.So, Owen got $48$ math questions right, out of the total $144$ questions he got right. $\newline$ To find out how many history questions he got right, we subtract the math questions from the total correct questions. $\newline$ $144 - 48 = 96$ history questions correct.Now we need to find out what percent $96$ is of the total history questions. $\newline$ We already calculated that $55\%$ of the questions were history, so $55\%$ of $200$ is $(55/100) \times 200$ .Calculating that gives us $48$ $0$ questions in history.Finally, to find the percent of history questions Owen got right, we divide the number of correct history answers by the total number of history questions and multiply by $48$ $1$ . $\newline$ $48$ $2$ , which we round to $48$ $3$ .