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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

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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.

Answer: A

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