Question

Delaney has 4 times as many books as she has movies. If she buys 15 more movies ( but no more books ), her ratio of movies to books will be 2:3. How many movies and how many books does she currently have?

Answer 1

The present number of movies does Delaney has is 9

The present number of Books does Delaney has is 36 .

Explanation:

Given as :

The number of books = 4 time number of movies

Let The number of books = B

Let The number of movies = M

So, B = 4 × M .......1

Again

If 15 more movies bought , the ratio of movies to books = 2 : 3

I.e The number of movies = M' = M + 15

So,
`(M')/(B)` =
`(2)/(3)`

Or,
`(M + 15)/(B)` =
`(2)/(3)`

Or, 3 × (M + 15) = 2 × B

Or, 3 M + 45 = 2 B ........2

Solving eq 1 and eq 2

i.e 3 M + 45 = 2 × 4 × M

Or, 8 M - 3 M = 45

Or, 5 M = 45

∴ M =
`(45)/(5)`

i.e M = 9

So, The number of movies = M = 9

Now, putting the value of M into eq 1

∵ B = 4 × M

So, B = 4 × 9

i.e B = 36

So, The number of books = B = 36

Hence, The present number of movies does Delaney has is 9 and The present number of Books does Delaney has is 36 . Answer