Question

Galvin bought 3/5 as many non-fiction books as fiction books from a book fair. He read 6 non-fiction books and 13 fiction books. He then had 3/4 as many non-fiction books left to read as fiction books. How many books did Galvin buy altogether?

Answer 1

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Answer 2

Answer:  Number of books Galvin bought altogether is 168.

Step-by-step explanation:

Since we have given that

Let the number of fiction books be 'x'

Let the number of non-fiction books is given by

$\frac{3}{5}x$

Number of non-fiction books he read = 6

Number of fiction books he read = 13

Now, According to question, we have given that He had $\frac{3}{4}$ as many non-fiction books left to read as fiction books.

Let the fiction books he has left be 'y'.

Let the non-fiction books he has left is given by

$\frac{3}{4}y$

Now, our equation becomes,

$x-13=y-------(1)\\\\and\\\\\frac{3}{5}x+6=\frac{3}{4}y-----------------(2)$

Now. put the value of Eq(1) in Eq(2), we get,

$\frac{3}{5}x+6=\frac{3}{4}(x-13)\\\\\frac{3}{5}x+6=\frc{3}{4}x-\frac{39}{4}\\\\(\frac{3}{5}-\frac{3}{4})x=\frac{-39}{4}-6\\\\\frac{12-15}{20}x=\frac{-39-24}{4}\\\\\frac{-3}{20}x=\frac{-63}{4}\\\\x=\frac{63}{4}\times \frac{20}{3}\\\\x=21\times 5\\\\x=105$

So, Number of fiction books = 105

Number of non- fiction books is given by

$\frac{3}{5}\times 105\\\\=3\times 21\\\\=63$

Hence, Number of books Galvin bought altogether is given by

$105+63=168$