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

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Manager
Joined: 16 Jul 2009
Posts: 227
If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4 [#permalink]

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08 Jun 2010, 10:30
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95% (hard)

Question Stats:

52% (03:55) correct 48% (03:26) wrong based on 282 sessions

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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. Math Expert Joined: 02 Sep 2009 Posts: 45305 Re: m21 #32 [#permalink] ### Show Tags 08 Jun 2010, 11:00 7 This post received KUDOS Expert's post 2 This post was BOOKMARKED 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 $$2d+2p=28c$$ --> $$p+28c=p+2d+2p=2d+3p=2d+3*\frac{5d}{3}=7d$$.

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Manager
Joined: 16 Jul 2009
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08 Jun 2010, 12:36
Thanks again bunnel! Your explanations just make them look really simple..

Intern
Joined: 05 Jun 2016
Posts: 18
GMAT 1: 760 Q51 V41
Re: If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4 [#permalink]

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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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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

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