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In a class of 90 students, children play football, cricket and badminton.55 play cricket,53 play football,35 play badminton.25 play cricket and football,13 play cricket and badminton and 3 play all three sports.How many will get a certificate for only football?

 Aug 10, 2022
 #1
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If we plot the given info in a Venn diagram, it would look like this: 

 

 

We will first solve for the number of people who only play cricket. 

 

Since we know the total is 55, we can write an equation: \(c + 13 + 3 + 25 = 55\), meaning \(c =14\)

 

Next, we know that \(b + x + 16 = 35\) and \(f + x + 28 = 53\)

 

But, knowing that there are 90 students in total, we can write the equation \(b + x + f = 90\)

 

Now, just solve for f. Hint: Simplify the equations and substitute 1 into another

 Aug 10, 2022

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