The number of picture books does Annette have is 76 books.
Given the ratio of picture books , encyclopedias and fairy tales books is 3:4:5 and she have half of her encyclopedias to her brother and he gave her 5 books of fairytales
We need to find the number of picture books does she have
According to the statement the total number of books does Annette have is
3k+4k+5k = 12k
Where k is total number of books
Now , Picture book she have = 3/12k = 1/4k
Encyclopedia she have = 4/12k = 1/3k
Fairy tale she have = 5/12k
Here,
Encyclopedia +14 = Fairy tale
Substituting the values of Encyclopedia and Fairy tale
(1/3 -1/2)k +14 = (5/12k -5 )
Therefore.
(1/6k+14) = (5k/12-5)
Therefore,
14+5 = 5k/12 - k/6
Therefore,
19 = 3k/12
19*4=k
76 = k
Here k = 76 books
Hence the total number of picture books does she have is 76
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