Question

Of my books, 85% are new and the rest are used. Some are biographies, 70% of which are new. What is the ratio of the fraction of new books that are biographies to the fraction of used books that are biographies?
A. 7:17
B: 14:17
C: 17:14
D: 17:7

Answer 1

wait let me reanalyze lol

Answer 2

please tell me you've discussed "trees" or something that looks like it

Answer 3

I don't think so. The only tree that I can think of is the one used in probability.

Answer 4

how about the set theory thingy in statistics? the ones with the \(A\cap B\) familiar?

Answer 5

because those things are the only ways i see to solve this

Answer 6

I'm starting 8th grade this September.
I'm not sure what you are talking about.

Answer 7

darn. i can't narrow down my thought process

Answer 8

maybe @terenzreignz will think of something before I do

Answer 9

Help me TJ! D:

Answer 10

Still thinking...

Answer 11

I got this from the 2012-2013 Annual 7th Grade contest. I took it, and I did pretty bad... >_> I'm just checking how I can solve these problems, so that I can solve it later on.

Answer 12

hmm... books... 85% new...15% used

bios...70% new...30% used

new books bio/ used books bio

hmm...

let me post this...it helps my thought process

Answer 13

Alright. I wish I have your brain. I try everything in my head. Well, I kind of have to in this contest because there's no room! T~T

Answer 14

Okay... I have an idea.

Answer 15

Fraction of new books that are biographies =
number of new biographies OVER number of new books.

Answer 16

Is it (70/85)?

Answer 17

^I doubt that's the answer though.

Answer 18

Strictly speaking, it's
\[\Large \frac{0.7 \times <number \ of \ biographies>}{0.85}\]

Answer 19

if simplfied it matches one of the choices though

Answer 20

And no, that's not the answer yet.

Answer 21

I meant that's not number of new biographies over number of new books.

Answer 22

But that <number of biographies> will be irrelevant once you consider the other fraction:
Fraction of used books that are biographies =
number of used biographies OVER number of used books

Answer 23

Sorry... it would be
\[\Large \frac{0.3\times <number \ of \ biographies>}{0.15}\]

Answer 24

that doesn't match the choice though...i think it gives 7/16

Answer 25

Patience, people :D

Answer 26

nevermind

Answer 27

it was a typographical error...it does match

Answer 28

ahahaha
@xlegendx
;)

Answer 29

My head hurt. T~T
I do not understand what you mean by number of biographies.

Answer 30

I mean, it wasn't specified, so the actual fraction would be (for the second one) 30% OF THE BIOGRAPHIES divided by the total number of used books :)

Answer 31

Don't worry, it's just an unknown number that will prove irrelevant once we get to the next step... anytime you're ready :D

Answer 32

I understand.

Answer 33

Okay, great :)
We now have the two fractions, and we need the ratio between them.
Let's let me have an easier time and represent the <number of biographies> simply as b, shall we?
\[\Large \frac{0.7\times b}{0.85}:\frac{0.3\times b}{0.15}\]

Answer 34

Okay. :)

Answer 35

So, that means b is a common factor of the left part and the right part of the ratio, it means it may be cancelled out :D

Answer 36

Got that part? That's about the last tricky part of this question.

Answer 37

Hmm. I believe so.

Answer 38

To illustrate, the ratio
\[2\times \color{red}3 : 3\times \color{red}3\]
is the same as the ratio
\[2 : 3\]
ie the common factor of 3 may be cancelled out.
It's like reducing to lowest terms, yeah? :D

Answer 39

Yeah!

Answer 40

Okay, let's get this done... cancelling out the common factor b, we get the "not so" simple ratio
\[\Large \frac{0.70}{0.85}: \color{red}{\frac{0.30}{0.15}}\]

Answer 41

We could multiply both sides of the ratio by
\[\Large \frac{100}{100}=1\]To make things simpler...

Answer 42

I see.

Answer 43

Giving us...
\[\Large \frac{70}{85}:\frac{30}{15}\]
Carry on from here?

Answer 44

Hmm.
70 * 15 =1050
85 * 30 = 2550

1050:2550 = 7:17

Answer 45

Awww yeaaahh
:D

Answer 46

:D

Answer 47

Is this suppose to be a 7th grade level?!

Answer 48

I'm pretty sure I did something like this back in 6th :3

Answer 49

Wowow! This seem so difficult. I've done this before.