In a survey of 400 students in a school, 100 were found as drinking apple juice, 150 as drinking orange juice and 75 drinking both apple and orange juice. Find how many students drink neither apple nor orange juice.
Question
In a survey of 400 students in a school, 100 were found as drinking apple juice, 150 as drinking orange juice and 75 drinking both apple and orange juice. Find how many students drink neither apple nor orange juice.
Solution
To solve this problem, we need to understand that some students may drink both apple and orange juice. Here are the steps to find out how many students drink neither apple nor orange juice:
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First, find the total number of students who drink apple juice or orange juice. This is given as 100 (apple juice drinkers) + 150 (orange juice drinkers) = 250 students.
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However, we've counted the students who drink both juices twice, once in the apple juice count and once in the orange juice count. So, we need to subtract the number of students who drink both juices. This is given as 75 students.
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So, the total number of students who drink either apple juice, orange juice, or both is 250 (from step 1) - 75 (from step 2) = 175 students.
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Now, to find the number of students who drink neither apple nor orange juice, we subtract the number of students who drink either juice (or both) from the total number of students. This is given as 400 (total students) - 175 (from step 3) = 225 students.
So, 225 students drink neither apple nor orange juice.
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