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?

Question

Damon Alvarado

Social Studies

16 January, 05:33

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?

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Answers (1)

Know the Answer?

Brayden · Answer 1

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