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- danc
- Students
- Posts: 42
- Joined: Thu Oct 16, 2014 9:00 am
Word Problems book, Hard Question set, #13
I think there is a mistake in the answer explanation. After converting the ratios to make them equal O:M:D = 60:15:24, the answer explanation flips the two values for M and D at the top of page 209. M/D is listed as 24/15 but I think it should be 15/24. The answer to the question would then be 10/8 or any equivalent fraction rather than 16/5 as the book states. Is that right?
- n00bpron00bpron00b
- Students
- Posts: 89
- Joined: Sun Apr 20, 2014 6:12 pm
Re: Word Problems book, Hard Question set, #13
Hey,
Let,
Ob = obeers
D = darbles
M = muxes
30 Ob = 12 D
Ob/D = 12/30
Ob/D = 2/5
Now,
5 M = 20 Ob
M/Ob = 20/5
M/Ob = 4/1
M : Ob : D
----- 2 : 5
4 : 1
So we multiply by 2 to make it equal
8 : 2 : 5
We want the ratio of 2 M / 1 D
2 (8) / 1 (5) = 16/5
Or the following way
30 Ob = 12 D
30 Ob/12 = D
5 Ob / 2 = D
5 M = 20 Ob
M = 20 Ob / 5
M = 4 Ob / 1
So 2 M will be 8 Ob/1
=> (8Ob/1) / (5Ob/2)
=> 16/5
hope this helps
Let,
Ob = obeers
D = darbles
M = muxes
30 Ob = 12 D
Ob/D = 12/30
Ob/D = 2/5
Now,
5 M = 20 Ob
M/Ob = 20/5
M/Ob = 4/1
M : Ob : D
----- 2 : 5
4 : 1
So we multiply by 2 to make it equal
8 : 2 : 5
We want the ratio of 2 M / 1 D
2 (8) / 1 (5) = 16/5
Or the following way
30 Ob = 12 D
30 Ob/12 = D
5 Ob / 2 = D
5 M = 20 Ob
M = 20 Ob / 5
M = 4 Ob / 1
So 2 M will be 8 Ob/1
=> (8Ob/1) / (5Ob/2)
=> 16/5
hope this helps
- danc
- Students
- Posts: 42
- Joined: Thu Oct 16, 2014 9:00 am
Re: Word Problems book, Hard Question set, #13
That doesn't answer my question.
Last edited by danc on Sat Nov 29, 2014 3:06 pm, edited 1 time in total.
- n00bpron00bpron00b
- Students
- Posts: 89
- Joined: Sun Apr 20, 2014 6:12 pm
Re: Word Problems book, Hard Question set, #13
30 O = 12 D
Dividing by D on both sides
(30 O) / D = (12 D)/D
=> (30 O) / D = 12
re write this as
O/D * 30 = 12
Dividing by 30 on both sides
O/D = 12/30
D/O will be 30/12 not O/D
Dividing by D on both sides
(30 O) / D = (12 D)/D
=> (30 O) / D = 12
re write this as
O/D * 30 = 12
Dividing by 30 on both sides
O/D = 12/30
D/O will be 30/12 not O/D
- danc
- Students
- Posts: 42
- Joined: Thu Oct 16, 2014 9:00 am
Re: Word Problems book, Hard Question set, #13
Tommy, please help.
Last edited by danc on Sat Nov 29, 2014 3:06 pm, edited 1 time in total.
- n00bpron00bpron00b
- Students
- Posts: 89
- Joined: Sun Apr 20, 2014 6:12 pm
Re: Word Problems book, Hard Question set, #13
It's simple Algebra.
Anyways Tommy can provide you better clarity on it.
Anyways Tommy can provide you better clarity on it.
- danc
- Students
- Posts: 42
- Joined: Thu Oct 16, 2014 9:00 am
Re: Word Problems book, Hard Question set, #13
I get it now. Thanks.
Last edited by danc on Sun Nov 30, 2014 5:56 pm, edited 2 times in total.
- tommywallach
- Manhattan Prep Staff
- Posts: 1917
- Joined: Thu Mar 31, 2011 11:18 am
Re: Word Problems book, Hard Question set, #13
Hey Dan,
I don't quite understand what part of the algebra you don't like here:
30 * O = 12 * D
If we divide both sides by 30, we get:
O = 12/30 * D
If we divide both sides by D, we get:
O/D = 12/30
In what way are we flipping the values of the variables?
-t
P.S. Try not to lash out at others who are trying to help. I understand that a lot of explanations here on the forums are not fantastic, and you're totally welcome to ask for me to step in (I always will!). But part of the fun is that it's a discussion, not just me answering questions for people. Thanks!
I don't quite understand what part of the algebra you don't like here:
30 * O = 12 * D
If we divide both sides by 30, we get:
O = 12/30 * D
If we divide both sides by D, we get:
O/D = 12/30
In what way are we flipping the values of the variables?
-t
P.S. Try not to lash out at others who are trying to help. I understand that a lot of explanations here on the forums are not fantastic, and you're totally welcome to ask for me to step in (I always will!). But part of the fun is that it's a discussion, not just me answering questions for people. Thanks!
- tommywallach
- Manhattan Prep Staff
- Posts: 1917
- Joined: Thu Mar 31, 2011 11:18 am
Re: Word Problems book, Hard Question set, #13
Hey Dan,
I see what you're mistaking. You think the sentence:
The value of 30 oobers equals the value of 12 darbles
MEANS
The ratio of Oobers to darbles is 30 to 12
Unfortunately, they are not the same thing. Keep in mind that the original sentence says nothing about ratios, so you're jumping to a conclusion there. If it helps, think of it this way, if the value of 30 oobers equals the value of 12 darbles, which is worth more, darbles or oobers? Clearly, darbles are worth more (because you only need 12 of them to equal 30 oobers). This means that the ratio of Oobers to Darbles should favor Darbles, because they are worth more.
If that doesn't help, all you really need to know is that ratios have to be expressed with division. This is why the book jumps immediately to division. The ratio of Oobers to Darbles must be expressed as O/D. So we should solve our original equation to have O/D on one side, as that represents the ratio of Oobers to Darbles.
Hope that makes it clearer!
-t
I see what you're mistaking. You think the sentence:
The value of 30 oobers equals the value of 12 darbles
MEANS
The ratio of Oobers to darbles is 30 to 12
Unfortunately, they are not the same thing. Keep in mind that the original sentence says nothing about ratios, so you're jumping to a conclusion there. If it helps, think of it this way, if the value of 30 oobers equals the value of 12 darbles, which is worth more, darbles or oobers? Clearly, darbles are worth more (because you only need 12 of them to equal 30 oobers). This means that the ratio of Oobers to Darbles should favor Darbles, because they are worth more.
If that doesn't help, all you really need to know is that ratios have to be expressed with division. This is why the book jumps immediately to division. The ratio of Oobers to Darbles must be expressed as O/D. So we should solve our original equation to have O/D on one side, as that represents the ratio of Oobers to Darbles.
Hope that makes it clearer!
-t
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