RATIOS QUESTION INQUIRY

[GonzaloB919]

HI! TAKING ONE CAT I FACED THIS QUESTION... I AM WONDERING WHAT HAPPENS IF THE QUESTION ASK ME TO HALF THE RELATIONSHIP BETWEEN F & R BESIDES DOUBLE H&R?? I WOULD APPRECIATE YOUR COMMENTS..

Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 3 fantasy books, there are 5 reference books. If the proportion of history to reference books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?

ANSWER: 19%

[RonPurewal]

HI! TAKING ONE CAT I FACED THIS QUESTION... I AM WONDERING WHAT HAPPENS IF THE QUESTION ASK ME TO HALF THE RELATIONSHIP BETWEEN F & R BESIDES DOUBLE H&R?? I WOULD APPRECIATE YOUR COMMENTS..

please try not to use all capitals; that's the internet equivalent of yelling (and it's a lot harder to read, too).

you could do this, of course. the current ratio f:r is 3:5; if you cut that in half, it's 3:10.
the current ratio of h:r is 6:35; if you double that, it's 12:35.

the lowest common multiple of 10 and 35 is 70, so this is an overall ratio of f:h:r = 21:24:70.

[RonPurewal]

by the way, if you have any further questions, please post the FULL question exactly as originally displayed, including all answer choices (as specified in the forum rules).

even if the answer choices are not relevant to the specific question you're asking, you still need to do this. thank you.

[GonzaloB919]

Hi, thank you very much for your response. I will take in to account your advises about posting rules...Also, I apologize to anyone who could be offended. However, I have read in a similar problem from OG 2015 that when you double a ratio, also you have to reconsider the other relationship.. please, take a look of the following problem..

[redacted]

[RonPurewal]

please don't post OG problems. if you want to mention an OG problem, just cite the edition number and problem number.

thanks.

[RonPurewal]

Hi, thank you very much for your response. I will take in to account your advises about posting rules...Also, I apologize to anyone who could be offended. However, I have read in a similar problem from OG 2015 that when you double a ratio, also you have to reconsider the other relationship.. please, take a look of the following problem..

[redacted]

here's a similar problem: let's say the ratio of a:b:c is currently 4:10:50. you want to double the ratio a:b and halve the ratio a:c.

the point is that you can pull out any ratio of two of these, and treat it separately.
the ratio a:b is currently 4:10 = 2:5. you want to double this, so that it becomes 4:5.
the ratio a:c is currently 4:50 = 2:25. you want to halve this, so that it becomes 1:25.

now just put them back together, by making a common value for "a" (the one that's in both parts):
a:b = 4:5
a:c = 1:25 = 4:100
so
a:b:c = 4:5:100.

then, if you have specific values, you treat them as you would in any other ratio.

[subhis75]

Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 3 fantasy books, there are 5 reference books. If the proportion of history to reference books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?

Please review my solution to check where i went wrong.
2 H books => 7 F books
3 F books => 5 R books
so the ratios will be depicted as H:F = 7:2
F: R = 5:3
and H:F:R = 35: 10: 6
which is quite contrary to what others have worked upon. Isn't this the way the question is decoded?

I am confused because in the below problem i work ratios like that-
A cat leaps 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?
Given;
3 dog = 4 cat;
Or, dog/cat = 4/3; ( and not 3/4 )

[Sage Pearce-Higgins]

Well done for writing your solution clearly. Actually, you're making a simpler error than you probably expect. To translate the ratio "for every 2 history books, there are 7 fantasy books", we just want to write H:F is 2:7. (Think: which book is more numerous?). If you do that for the other ratio, your method will work out.