PS "A movie buff owns movies" question

Sorry, the questions is the following one (the ratio is 11:4 and not 11:14) :

A movie buff owns movies on DVD and on Blu-ray in a ratio of 7:2. If she buys 6 more Blu-ray movies, that ratio would change to 11:4. If she owns movies on no other medium, what was the original number of movies in her library before the extra purchase?

The answer. You just need to set two equations:

- D / B = 7/2
- D / (B+6) = 11/4

You then just need to solve for D and B.

pagalmes wrote:Sorry, the questions is the following one (the ratio is 11:4 and not 11:14) :

A movie buff owns movies on DVD and on Blu-ray in a ratio of 7:2. If she buys 6 more Blu-ray movies, that ratio would change to 11:4. If she owns movies on no other medium, what was the original number of movies in her library before the extra purchase?

Hi pagalmes,

I solved the equation like this:

1) D/B = 7/2, -->2D/7B = 1 -->2D=7B --> D=7B/2
2) D/ (B+6) = 11/4 --> (7B/2)/(B+6) = 11/4
3) 7B/2 = (11/4)*(B+6) --> 7B/2=(11B+66)/4 --> [4(7B)]/2=11B+66 --> 28B/2 = 11B+ 66 --> 14B=11B+66 --> 3B=66 --> B=22
4) D/22 = 7/2 --> D=(7*22)/2 --> D=154/2 --> D=77
5) D+B= 77+22 =99 movies

You could perform step 4 a little quicker by realizing that 2*11=22; therefore 7*11=x

Hope that helps.

I did this the same way as described by the above posts, but looking at the answer choices it looks like 99 could be the only choice. The ratio of 7:2 indicates that the original number would have to be divisible by 9. 99 is the only answer choice on the list that fits the original ratio.

Thanks for your answers!

pagalmes wrote:A movie buff owns movies on DVD and on Blu-ray in a ratio of 7:2. If she buys 6 more Blu-ray movies, that ratio would change to 11:14. If she owns movies on no other medium, what was the original number of movies in her library before the extra purchase?

- 22
- 28
- 77
- 99
- 105

Any idea how to solve that? I can't find the way to solve that question...

if the ratio is 11:4
so 7x/(2x+6) = 11/4 --> 28x = 22x +66 --> x=11
so original no. = 7x+2x=9x=99