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If 75 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?

Answer :

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Answer: 50% of the class answered both questions correctly

Explanation:

To find the percentage of the class that answered both questions correctly, we must first find the combined percentage of the class that answered question 1, question 2 or both questions correctly.

= Total percentage of the class - Percentage that didn't answer any of the 2 questions correctly

i.e 100%-20%=80%

Let's now denote x% for the percentage of the class that answered both questions correctly.

Meanwhile, percentage of the class that answered only question 1 correctly = 75-x% and percentage of the class that answered only question 2 correctly = 55-x%

Remember that % of those that answered only question 1 + % of those that answered only question 2 + % of those that got both answers correctly = 80%

= 75-x% + 55-x% + x%=80%

= 75-x + 55-x + x = 80

= 75 + 55 - x = 80

= 130 - x = 80

x = 50%

50% of the class answered both questions correctly

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