Question 1206823
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Let x be the number who read all three newspapers.  Then<br>
75-x = number who read Daily Times and Guardian but not Punch
54-x = number who read Guardian and Punch but not Daily Times
60-x = number who read Punch and Daily Times but not Guardian<br>
The number who read Daily Times only is (181) - ((75-x)+(60-x))-x = 46+x
The number who read Guardian only is (142) - ((75-x)+(54-x))-x = 13+x
The number who read Punch only is (117) - ((60-x)+54-x))-x = 3+x<br>
Every one of the 290 readers reads at least one of the three:<br>
(x)+(75-x)+(54-x)+(60-x)+(46+x)+(13+x)+(3+x)=290
251+x=290
x=39<br>
You can draw the Venn diagram and use it to answer the questions.<br>
Note that finding the number who read all three newspapers is found more easily using the inclusion-exclusion principle:<br>
(sum of numbers who read at least one) - (sum of numbers who read two of the three) + (number who read all three) = total<br>
(181+142+117)-(75+54+60)+x=290
440-189+x=290
261+x=290
x=39<br>