Math

QuestionIn a group of 146 students, 85 speak French and 83 speak Japanese. Find how many speak both languages.

Studdy Solution

STEP 1

Assumptions1. The total number of students is146. .85 students can speak French. 3.83 students can speak Japanese.
4. Every student speaks at least one language.
5. A student can speak both French and Japanese.

STEP 2

First, we need to find the total number of students who can speak either French or Japanese or both. This can be done by adding the number of students who can speak French and the number of students who can speak Japanese.
Total=Frenchspeakers+JapanesespeakersTotal = French\, speakers + Japanese\, speakers

STEP 3

Now, plug in the given values for the number of French speakers and Japanese speakers to calculate the total.
Total=85+83Total =85 +83

STEP 4

Calculate the total number of students who can speak either French or Japanese or both.
Total=85+83=168Total =85 +83 =168

STEP 5

Since every student speaks at least one language, the total number of students who can speak either French or Japanese or both should be equal to the total number of students. But we have more students in our calculation. This means that some students are counted twice because they can speak both languages. We can find the number of students who can speak both languages by subtracting the total number of students from our calculated total.
Bothlanguages=TotalcalculatedTotalstudentsBoth\, languages = Total\, calculated - Total\, students

STEP 6

Plug in the values for the calculated total and the total number of students to calculate the number of students who can speak both languages.
Bothlanguages=168146Both\, languages =168 -146

STEP 7

Calculate the number of students who can speak both languages.
Bothlanguages=168146=22Both\, languages =168 -146 =22So,22 students can speak both French and Japanese.

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