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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  [#permalink]

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New post 08 Oct 2018, 06:34
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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Re: If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4   [#permalink] 08 Oct 2018, 06:34
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