32 candidates took examinations at centre. 11 took french,9 took spanish and x took both,18 took neither subject

Question

1.Write an expression in x for the number of candidates in the universal set
2.Calculate the value of x

Answer 1

Use Venn diagrams

Draw two intersecting circles, label one French, the other Spanish

Place x in the overlap, 11-x in the non-overlapping part of the French circle and 9-x in the non-overlapping part of the Spanish circle. Put 18 outside the two circles.

11-x + x + 9-x + 18 = 32

solve for x=6