Answer:
(i) 145
(ii) 300
Explanation:
Given:
total students ... 500
like bananas ... 280
like apples ... 310
dislike fruits ... 55
(i) Find the number of students who like both fruits.
To find the number of students who like both fruits we first add students who like bananas and apples and then subtract students who like at least one fruit.
Students who like at least one of the fruits:
like fruit = total - dislike fruits
like fruit = 500 - 55 = 445
Students who like both fruits:
like both = (like bananas + like apples) - like fruit
like both = (280 + 310) - 445
like both = 145
(ii) Find the number of students who like only one fruit.
To find this we have to find how many students like ONLY bananas and ONLY apples.
like one fruit = like only apples + like only bananas
To find students who like only apples and like only bananas we subtract students who like both (calculated in (i)).
like only apples = like apples - like both = 310 - 145 = 165
like only bananas = like bananas - like both = 280 - 145 = 135
Therefore,
like one fruit = like only apples + like only bananas
like one fruit = 165 + 135
like one fruit = 300
(iii) Show the result in a Venn-diagram.
See attached picture.