GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 18 Feb 2020, 04:05

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

Hide Tags

Manager
Joined: 16 Jul 2009
Posts: 163
If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4  [#permalink]

Show Tags

08 Jun 2010, 09:30
2
19
00:00

Difficulty:

95% (hard)

Question Stats:

48% (03:34) correct 52% (03:23) wrong based on 330 sessions

HideShow timer Statistics

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: 61269 Re: m21 #32 [#permalink] Show Tags 08 Jun 2010, 10:00 7 3 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 $$2d+2p=28c$$ --> $$p+28c=p+2d+2p=2d+3p=2d+3*\frac{5d}{3}=7d$$.

_________________
General Discussion
Manager
Joined: 16 Jul 2009
Posts: 163

Show Tags

08 Jun 2010, 11:36
Thanks again bunnel! Your explanations just make them look really simple..

Intern
Joined: 05 Jun 2016
Posts: 19
GMAT 1: 760 Q51 V41
Re: If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4  [#permalink]

Show Tags

26 Nov 2016, 20:19
7p−5d35=d+p147p−5d35=d+p14 --> 105d = 63p, doesn't exactly equal to 5/3 though.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9426
Location: United States (CA)
Re: If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4  [#permalink]

Show Tags

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 181 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: 935 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.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4   [#permalink] 08 Oct 2018, 05:34
Display posts from previous: Sort by