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?

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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?

Calculate Total Correct Answers: Calculate the total number of questions Owen answered correctly. $\newline$ We know that Owen answered $72\%$ of all $200$ questions correctly. To find the total number of questions he answered correctly, we multiply $72\%$ by $200$ . $\newline$ Total correct answers = $72\%$ of $200$ $\newline$ Total correct answers = $0.72 \times 200$ $\newline$ Total correct answers = $144$
Calculate Math Questions: Calculate the number of math questions. $\newline$ We know that $45\%$ of the questions were math questions. To find the total number of math questions, we multiply $45\%$ by $200$ . $\newline$ Total math questions = $45\%$ of $200$ $\newline$ Total math questions = $0.45 \times 200$ $\newline$ Total math questions = $90$
Calculate Correct Math Answers: Calculate the number of math questions Owen answered correctly. $\newline$ We know that Owen answered $53.3\%$ of the math questions correctly. To find the number of math questions he answered correctly, we multiply $53.3\%$ by the total number of math questions. $\newline$ Correct math answers = $53.3\%$ of $90$ $\newline$ Correct math answers = $0.533 \times 90$ $\newline$ Correct math answers = $47.97$ $\newline$ Since the number of questions answered correctly cannot be a fraction, we round it to the nearest whole number. $\newline$ Correct math answers $\approx 48$
Calculate History Questions: Calculate the number of history questions. $\newline$ Since there are $200$ questions in total and $90$ are math questions, the rest are history questions. $\newline$ Total history questions $=$ Total questions $-$ Math questions $\newline$ Total history questions $=$ $200 - 90$ $\newline$ Total history questions $=$ $110$
Calculate Correct History Answers: Calculate the number of history questions Owen answered correctly. $\newline$ We know that Owen answered a total of $144$ questions correctly and $48$ of these were math questions. To find the number of history questions he answered correctly, we subtract the number of correct math answers from the total number of correct answers. $\newline$ Correct history answers $=$ Total correct answers $-$ Correct math answers $\newline$ Correct history answers $= 144 - 48$ $\newline$ Correct history answers $= 96$
Calculate Percentage of Correct History Answers: Calculate the percentage of history questions Owen answered correctly. $\newline$ To find the percentage, we divide the number of correct history answers by the total number of history questions and then multiply by $100$ . $\newline$ Percentage of correct history answers = $(\text{Correct history answers} / \text{Total history questions}) \times 100$ $\newline$ Percentage of correct history answers = $(96 / 110) \times 100$ $\newline$ Percentage of correct history answers $\approx 87.27\%$