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

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08 Jun 2010, 09:30
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Difficulty:

95% (hard)

Question Stats:

48% (03:34) correct 52% (03:21) wrong based on 216 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. ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 64249 Re: m21 #32 [#permalink] ### Show Tags 08 Jun 2010, 10:00 9 4 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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08 Jun 2010, 11:36
Thanks again bunnel! Your explanations just make them look really simple..

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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, 20:19
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, 10:26
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 _________________ # Scott Woodbury-Stewart Founder and CEO Scott@TargetTestPrep.com 202 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 937 Re: If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4 [#permalink] ### Show Tags 08 Oct 2018, 05:34 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

$$?\,\,\,:\,\,\,p + 28c = f\left( d \right)$$

$$\left( {\rm{I}} \right)\,\,5d + 35c = 7p$$

$$4d + 4p = 56c\,\,\,\, \Rightarrow \,\,\,\,\left( {{\rm{II}}} \right)\,\,d + p = 14c$$

$$\left\{ \matrix{ 2 \cdot \left( {\rm{I}} \right)\,\,\,\,10d + 70c = 14p\,\,\, \hfill \cr 5 \cdot \,\left( {{\rm{II}}} \right)\,\,\,5d + 5p = 70c \hfill \cr} \right.\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,\,15d = 9p\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,p = {5 \over 3}d\,\,\,\,\left( {{\rm{III}}} \right)$$

$$\left\{ \matrix{ \left( {\rm{I}} \right)\,\,\,\,5d + 35c = 7p\,\,\, \hfill \cr 7 \cdot \,\left( {{\rm{II}}} \right)\,\,\,7d + 7p = 98c \hfill \cr} \right.\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,\,12d = 63p\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,c = {4 \over {21}}d\,\,\,\,\left( {{\rm{IV}}} \right)$$

$$?\,\,:\,\,\,p + 28c\,\,\,\mathop = \limits^{{\text{III}}\,,\,\,{\text{IV}}} \,\,\,\,\frac{5}{3}d + 28\left( {\frac{4}{{21}}d} \right) = \frac{5}{3}d + \frac{{16}}{3}d = 7d\,\,\,\,\, \Rightarrow \,\,\,\,\boxed{\,\,? = \ 7\,\,}$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4  [#permalink]

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22 Feb 2020, 04:38
Here's the long version of the answer -
7p - 35c = 5d
4p - 56c = -4d
solve this (this is the only step that takes time)
we get 252c = 48d
or 126c = 24d
or 42 c = 8d (hold onto this)

4d + 4p = 56c
1d + 1p = 14c
so 1p = 14c - 1d
so 1p + 28c = 42c - 1d
using 42c = 8d

Answer = 1p + 28c = 7d

It takes around 2.5-3 minutes to solve
If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4   [#permalink] 22 Feb 2020, 04:38