SOLUTION: Fifty people said they liked apples or bananas or both. Forty per cent of the people like apples and 70% of the people like bananas. What percentage of people like only apples?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Fifty people said they liked apples or bananas or both. Forty per cent of the people like apples and 70% of the people like bananas. What percentage of people like only apples?      Log On


   

Question 1098049: Fifty people said they liked apples or bananas or both. Forty per cent of the people like apples and
70% of the people like bananas. What percentage of people like only apples?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
50 like apples or bananas or both.

40% like apples.
70% like bananas.

40% of 50 = 20
70% of 50 = 35

(a or b) = a + b - ab.

ab are the people who like both.

since (a or b) = 50, then:

50 = 20 + 35 - ab

solve for ab to get ab = 5

you have 20 like apples and 35 like bananas and 5 like both.

the 5 that like both are counted in the 20 that like apples and the 35 that like bananas, so strip them out and you have 15 like apples only and 30 like bananas only and 5 like both.

the percentage of people that like only apples is 15/50 = 30%.