Jack has a total of b hardback and paperback books in his library. If the number of hardback books is 1/3 the number of paperback books, and 3/4 of the of the paperback books are biographies, how many biographies, in terms of b, are in Jack's library?
A)(1/9)b
B)(3/20)b
C)(3/16)b
D)(1/3)b
E)(9/16)b
I honestly don't think any of the answers are correct. I will give the OA and explanation after some discussion.
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this is simple ratio problem, b is total and H (hardback)=P/3 (paperback), 3P/4=Biographies. P=3H and Biographies=3*3H/4=9H/4. Since b is total and consists of H and P, we have the following ratios P/H=3/1 and P+H=b=4 with b=4H --> Biographies=9H/4, H=b/4 and accordingly Biographies=9(b/4):4=9b/16
e
e
seal4913 wrote:Jack has a total of b hardback and paperback books in his library. If the number of hardback books is 1/3 the number of paperback books, and 3/4 of the of the paperback books are biographies, how many biographies, in terms of b, are in Jack's library?
A)(1/9)b
B)(3/20)b
C)(3/16)b
D)(1/3)b
E)(9/16)b
I honestly don't think any of the answers are correct. I will give the OA and explanation after some discussion.
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That is the OA and how they explain it. Here is my question, if you use the plug in method I don't see where I am making my mistake.
So say if you have 4 books that means 3 are soft and 1 is hard. Then the number of soft that are bios is 3 x (3/4) which is 9/4. The number of hard that are bios is 9/4s = bio so it's (9/4) x (1/3) which is 1/4. So is not my bio equal to 1/4 plus 9/4 which is 10/4?
So (9/16) * 4 = 9/4 but 9/4 is only the bios he has in soft... I fail to see it... please help
So say if you have 4 books that means 3 are soft and 1 is hard. Then the number of soft that are bios is 3 x (3/4) which is 9/4. The number of hard that are bios is 9/4s = bio so it's (9/4) x (1/3) which is 1/4. So is not my bio equal to 1/4 plus 9/4 which is 10/4?
So (9/16) * 4 = 9/4 but 9/4 is only the bios he has in soft... I fail to see it... please help
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We are given only: "3/4 of the of the paperback books are biographies".seal4913 wrote:The number of hard that are bios is 9/4s = bio ? so it's (9/4) x (1/3) which is 1/4.
Distinctively, we must have integer value for bios, i.e. this could not be 9/4 and b isn't 4. If you noticed I supplied
not culminating by 'b=4' and leaving with 'b=4H'. The distinction made is b=4H not b=4. Hence b could be 16, as bios=(9/16)*b=(3^2/2^4)*b and bios might be 9. If b=32, b would be 18, etc. We were required to find bios expressed through 'b' only.we have the following ratios P/H=3/1 and P+H=b=4 with b=4H
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The total of hardbacks and paperbacks is B; H + P = B
Hardbacks are 1/3 of the number of paperbacks: H = P/3
3/4 of paperbacks are biographies: 3P/4 = X
To solve for X, we need P in terms of B, which we can find by substituting our second equation into the first equation:
H + P = B
P/3 + P = B
4P/3 = B
4P = 3B
P = 3B/4
We can then substitute into the third equation:
3P/4 = X
3(3B/4) / 4 = X
(9B/4)/4 = X
9B/16 = X
Hardbacks are 1/3 of the number of paperbacks: H = P/3
3/4 of paperbacks are biographies: 3P/4 = X
To solve for X, we need P in terms of B, which we can find by substituting our second equation into the first equation:
H + P = B
P/3 + P = B
4P/3 = B
4P = 3B
P = 3B/4
We can then substitute into the third equation:
3P/4 = X
3(3B/4) / 4 = X
(9B/4)/4 = X
9B/16 = X
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We are given that Jack as a total of b hardback and paperback books in his library. We can let h = the number of hardback books and p = the number of paperback books, and thus h + p = b.seal4913 wrote:Jack has a total of b hardback and paperback books in his library. If the number of hardback books is 1/3 the number of paperback books, and 3/4 of the of the paperback books are biographies, how many biographies, in terms of b, are in Jack's library?
A)(1/9)b
B)(3/20)b
C)(3/16)b
D)(1/3)b
E)(9/16)b
We know that the number of hardback books is 1/3 the number of paperback books, and thus:
h = (1/3)p
We can now substitute (1/3)p for h in the equation h + p = b:
(1/3)p + p = b
Multiplying the entire equation by 3, we have:
p + 3p = 3b
4p = 3b
p = 3b/4
Finally, we are given that 3/4 of the paperback books are biographies. Since p = 3b/4, we have:
(3/4)(3b/4) = biographies
9b/16 = biographies
Answer: E
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