• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If 5 dollars and 35 crowns is equivalent to 7 pounds, and tagged by: nonplus2 ##### This topic has 2 expert replies and 0 member replies ### Top Member ## If 5 dollars and 35 crowns is equivalent to 7 pounds, and ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult 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? A.$7.00
B. $7.50 C.$8.50
D. $9.00 E.$10.00

### GMAT/MBA Expert

GMAT Instructor
Joined
09 Oct 2010
Posted:
729 messages
Followed by:
26 members
59
nonplus2 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?

A. $7.00 B.$7.50
C. $8.50 D.$9.00
E. $10.00 $$?\,\,\,:\,\,\,p + 28c = f\left( d \right)$$ $$\left( {\text{I}} \right)\,\,5d + 35c = 7p$$ $$4d + 4p = 56c\,\,\,\, \Rightarrow \,\,\,\,\left( {{\text{II}}} \right)\,\,d + p = 14c$$ $$\left\{ \matrix{ 2 \cdot \left( {\rm{I}} \right)\,\,\,\,10d + 70c = 14p\,\,\, \hfill \cr 5 \cdot \,\left( {{\rm{II}}} \right)\,\,\,5d + 5p = 70c \hfill \cr} \right.\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,\,15d = 9p\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,p = {5 \over 3}d\,\,\,\,\left( {{\rm{III}}} \right)$$ $$\left\{ \matrix{ \left( {\rm{I}} \right)\,\,\,\,5d + 35c = 7p\,\,\, \hfill \cr 7 \cdot \,\left( {{\rm{II}}} \right)\,\,\,7d + 7p = 98c \hfill \cr} \right.\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,\,12d = 63p\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,c = {4 \over {21}}d\,\,\,\,\left( {{\rm{IV}}} \right)$$ $$?\,\,:\,\,\,p + 28c\,\,\,\mathop = \limits^{{\text{III}}\,,\,\,{\text{IV}}} \,\,\,\,\frac{5}{3}d + 28\left( {\frac{4}{{21}}d} \right) = \frac{5}{3}d + \frac{{16}}{3}d = 7d\,\,\,\,\, \Rightarrow \,\,\,\,\boxed{\,\,? = \ 7\,\,}$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: https://GMATH.net (Math for the GMAT) Testimonials :: https://GMATH.net/testimonials.html Course release PROMO : finish our test drive till 31/Oct with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 60% discount! ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1651 messages Followed by: 14 members Upvotes: 43 nonplus2 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? A.$7.00
B. $7.50 C.$8.50
D. $9.00 E.$10.00
To solve this problem, we need to determine the equivalent of 1 pound to dollars and 1 crown to dollars. Let c = value of 1 crown in dollars and p = value of 1 pound in dollars. So we have:

5 + 35c = 7p

4 + 4p = 56c

We can simplify the second equation as 1 + p = 14c. Isolating p, we have p = 14c - 1. Substituting this back in the first equation, we have:

5 + 35c = 7(14c - 1)

5 + 35c = 98c - 7

12 = 63c

c = 12/63 = 4/21 dollars

Since c = 4/21, p = 14 x 4/21 - 1 = 2 x 4/3 - 1 = 8/3 - 3/3 = 5/3 dollars

Therefore, 1 pound and 28 crowns = 1 x 5/3 + 28 x 4/21 = 5/3 + 4 x 4/3 = 5/3 + 16/3 = 21/3 = 7 dollars.

_________________
Scott Woodbury-Stewart Founder and CEO

• Award-winning private GMAT tutoring
Register now and save up to $200 Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

### Top First Responders*

1 fskilnik@GMATH 74 first replies
2 Jay@ManhattanReview 49 first replies
3 Brent@GMATPrepNow 47 first replies
4 GMATGuruNY 43 first replies
5 Rich.C@EMPOWERgma... 36 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 fskilnik@GMATH

GMATH Teacher

195 posts
2 Scott@TargetTestPrep

Target Test Prep

183 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

123 posts
4 Max@Math Revolution

Math Revolution

89 posts
5 GMATGuruNY

The Princeton Review Teacher

87 posts
See More Top Beat The GMAT Experts