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Difficulty:
35%
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Question Stats:
73% (02:03) correct
27%
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wrong
based on 535
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The number of coins that Lana and Brad had were in the ratio of 5 : 2, respectively. After Lana gave Brad 8 of her coins, the ratio of the number of coins Lana had to the number Brad had was 3 : 2. As a result of this gift, Lana had how many more coins than Brad?
(A) 30
(B) 28
(C) 22
(D) 14
(E) 8
The answer is D. Is this correct - if you ask me - No. For me the answer should be (A). And here is my reasoning behind A. So can you please advise where I have gone wrong?
\(\frac{L}{B} = \frac{5}{2}\) --------------------------------------(1)
\(\frac{L-8}{B+8} = \frac{3}{2}\) ----------------------------------(2)
2L-16 = 3B+24
2L-3B = 40 ----------------------------------------------------------------------------------(3)
From 1 ------------------ 2L=5B
Putting the above in equation 3 will give 2B=40 and B = 20
Substituting the value of B in equation 2 will give L = 50
So the answer should be L - B = 50-20 = 30
(A) 30
(B) 28
(C) 22
(D) 14
(E) 8
The answer is D. Is this correct - if you ask me - No. For me the answer should be (A). And here is my reasoning behind A. So can you please advise where I have gone wrong?
\(\frac{L}{B} = \frac{5}{2}\) --------------------------------------(1)
\(\frac{L-8}{B+8} = \frac{3}{2}\) ----------------------------------(2)
2L-16 = 3B+24
2L-3B = 40 ----------------------------------------------------------------------------------(3)
From 1 ------------------ 2L=5B
Putting the above in equation 3 will give 2B=40 and B = 20
Substituting the value of B in equation 2 will give L = 50
So the answer should be L - B = 50-20 = 30
16 Mar 2012, 09:09
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enigma123
Given: \(\frac{L}{B}=\frac{5x}{2x}\), for some positive multiple \(x\) and \(\frac{5x-8}{2x+8}=\frac{3}{2}\) --> \(x=10\) --> \(L=50\) and \(B=20\).
Question: \((L-8)-(B+8)=?\) --> \((L-8)-(B+8)=14\).
Answer: D.
The problem with your solution is that you answered to the wrong question. The question is: "as a result of this gift, Lana had how many more stamps than Brad?" So, we need to find \((L-8)-(B+8)\) not \(L-B\).
Hope it's clear.
P.S. Check and edit whether the questions talks about the coins or stamps.
General Discussion
18 Mar 2012, 12:50
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This is how I did it:
Given information:
Lana's initial ratio = 5/7
Lana's ratio after giving 8 away = 3/5
So the formula is:
5/7x - 8 = 3/5x
x = 70 (which is the total # of stamps)
Since we know that Lana's new ratio = 3/5x, and Brad's ratio is 3/2x
Then plug in x into 3/5x and 3/2x to find out how many stamps each person has. Then subtract the two numbers to find out how many more stamps Lana has than Brad.
Given information:
Lana's initial ratio = 5/7
Lana's ratio after giving 8 away = 3/5
So the formula is:
5/7x - 8 = 3/5x
x = 70 (which is the total # of stamps)
Since we know that Lana's new ratio = 3/5x, and Brad's ratio is 3/2x
Then plug in x into 3/5x and 3/2x to find out how many stamps each person has. Then subtract the two numbers to find out how many more stamps Lana has than Brad.
