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If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4

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If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4  [#permalink]

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New post 08 Jun 2010, 10:30
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If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4 dollars and 4 pounds is equivalent to 56 crowns, 1 pound and 28 crowns is equivalent to how many dollars?

$7.00
$7.50
$8.50
$9.00
$10.00

m21 q32

Would like to understand the solving of the linear equations for the values of 'p' and 'c' given in the solution.
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Re: m21 #32  [#permalink]

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New post 08 Jun 2010, 11:00
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abhi758 wrote:
If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4 dollars and 4 pounds is equivalent to 56 crowns, 1 pound and 28 crowns is equivalent to how many dollars?

$7.00
$7.50
$8.50
$9.00
$10.00

Would like to understand the solving of the linear equations for the values of 'p' and 'c' given in the solution.


\(5d+35c=7p\) --> \(c=\frac{7p-5d}{35}\);
\(4d+4p=56c\) --> \(c=\frac{d+p}{14}\), also if we reduce this equation by 2 we'll get: \(2d+2p=28c\);

\(\frac{7p-5d}{35}=\frac{d+p}{14}\) --> \(3p=5d\) --> \(p=\frac{5d}{3}\).

\(p+28c=?\) --> as \(2d+2p=28c\) --> \(p+28c=p+2d+2p=2d+3p=2d+3*\frac{5d}{3}=7d\).

Answer: A.
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Re: m21 #32  [#permalink]

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New post 08 Jun 2010, 12:36
Thanks again bunnel! Your explanations just make them look really simple.. :)

Bunnel, would request you to add this thread link to this thread (gmat-test-m21-master-thread-all-discussions-78464.html) so that future M21 test takers can refer back to this solution instead of posting a fresh query.
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Re: If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4  [#permalink]

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New post 26 Nov 2016, 21:19
7p−5d35=d+p147p−5d35=d+p14 --> 105d = 63p, doesn't exactly equal to 5/3 though.
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Re: If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4  [#permalink]

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New post 30 Jan 2018, 11:26
abhi758 wrote:
If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4 dollars and 4 pounds is equivalent to 56 crowns, 1 pound and 28 crowns is equivalent to how many dollars?

$7.00
$7.50
$8.50
$9.00
$10.00



To solve this problem, we need to determine the equivalent of 1 pound to dollars and 1 crown to dollars. Let d = value of 1 dollar, c = value of 1 crown and p = value of 1 pound. We are given that:

5d + 35c = 7p

4d + 4p = 56c

We can simplify the second equation as d + p = 14c. Let’s isolate d in each equation:

5d = 7p - 35c → [1]

d = -p + 14c → [2]

If we multiply equation [2] by 7 and add that to equation [1], we have:

12d = 63c

c = 12d/63 = 4d/21

Similarly, if we multiply equation [1] by 2 and equation [2] by 5 and add those together, we have:

15d = 9p

p = 15d/9 = 5d/3

Thus, 1 pound and 28 crowns is equivalent to:

5d/3 + 28 x 4d/21 = 5d/3 + 16d/3 = 21d/3 = 7d or 7 dollars

Answer: A
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Re: If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4 &nbs [#permalink] 30 Jan 2018, 11:26
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