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the number of students who study only French = f;

the number of students who study only Spanish = s;

the number of students who study both French & Spanish = b;

Thus,

the number of students who study French = f + b;

the number of students who study Spanish = s + b;

the number of students who study neither French nor Spanish = n = b (given)

=> f + s + b + n = 200 => f + s + 2b = 200 ---(1)

Given 'One-quarter of those who study Spanish also study French,' we have (s + b)/4 = b => s = 3b ---(2)

Given 'The total number who study French is 10 fewer than those who study Spanish only,' we have f + b = s - 10 => s = f + b + 10 ---(3)

From (2) and (3), we have f + b + 10 = 3b => f = 2b - 10 ---(4)

From (1) and (4), we have

f + s + 2b = 200

=> 2b - 10 + 3b + 2b = 200

b = 30

Thus, f = 2b - 10 = 2*30 - 10 = 5

Hope this helps!

sorry not sure

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