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16 Sep 2014, 01:15
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If 5 dollars plus 35 crowns are equivalent to 7 pounds, and 4 dollars plus 4 pounds are equivalent to 56 crowns, then what is the equivalent amount in dollars for 1 pound plus 28 crowns?
A. $7.00
B. $7.50
C. $8.50
D. $9.00
E. $10.00
A. $7.00
B. $7.50
C. $8.50
D. $9.00
E. $10.00
16 Sep 2014, 01:15
Kudos
Bookmarks
Official Solution:
If 5 dollars plus 35 crowns are equivalent to 7 pounds, and 4 dollars plus 4 pounds are equivalent to 56 crowns, then what is the equivalent amount in dollars for 1 pound plus 28 crowns?
A. $7.00
B. $7.50
C. $8.50
D. $9.00
E. $10.00
The question asks us to find an equivalent amount in dollars for a combination of 1 pound and 28 crowns. In other words, we need to express \(p + 28c\) in terms of \(d\).
Given:
\(5d + 35c = 7p\), which can be rewritten as \(c = \frac{7p - 5d}{35}\);
\(4d + 4p = 56c\), which can be rewritten as \(c = \frac{d + p}{14}\).
By equating the two expressions for \(c\), we get \(\frac{7p - 5d}{35} = \frac{d + p}{14}\). Simplifying this equation yields \(p = \frac{5d}{3}\).
From the equation \(4d + 4p = 56c\), we can also deduce that \(2d + 2p = 28c\).
Since we now know that \(p = \frac{5d}{3}\) and \(28c = 2d + 2p\), we can express \(p + 28c\) as \(p + (2d + 2p) = 2d + 3p = 2d + 3* \frac{5d}{3} = 7d\).
Therefore, the equivalent amount in dollars for 1 pound and 28 crowns is \(7d\).
Answer: A
If 5 dollars plus 35 crowns are equivalent to 7 pounds, and 4 dollars plus 4 pounds are equivalent to 56 crowns, then what is the equivalent amount in dollars for 1 pound plus 28 crowns?
A. $7.00
B. $7.50
C. $8.50
D. $9.00
E. $10.00
The question asks us to find an equivalent amount in dollars for a combination of 1 pound and 28 crowns. In other words, we need to express \(p + 28c\) in terms of \(d\).
Given:
\(5d + 35c = 7p\), which can be rewritten as \(c = \frac{7p - 5d}{35}\);
\(4d + 4p = 56c\), which can be rewritten as \(c = \frac{d + p}{14}\).
By equating the two expressions for \(c\), we get \(\frac{7p - 5d}{35} = \frac{d + p}{14}\). Simplifying this equation yields \(p = \frac{5d}{3}\).
From the equation \(4d + 4p = 56c\), we can also deduce that \(2d + 2p = 28c\).
Since we now know that \(p = \frac{5d}{3}\) and \(28c = 2d + 2p\), we can express \(p + 28c\) as \(p + (2d + 2p) = 2d + 3p = 2d + 3* \frac{5d}{3} = 7d\).
Therefore, the equivalent amount in dollars for 1 pound and 28 crowns is \(7d\).
Answer: A
30 May 2016, 04:53
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Bunuel
Strategy in such questions is to eliminate each variable one by one.
First Form equations:
Eq. 1: 5d+35c = 7p
Eq. 2 : 4d+4p = 56c
Eliminate 1 variable
From eq 1: p = (5/7)d+5c
Put this in Eq 2:
4d+4{(5/7)d+5c} = 56 c
4d+ (20/7)d+ 20 c = 56 c
(48/7) d = 36 c
c = (4/21)d
Express p also in terms of d
p = (5/7)d+5c
p = (5/7)d+ 5 (4/21) d = (15/21) d + (20/21) d = (35/21) d = (5/3)d
Now come to the question once again: 1 pound and 28 crowns is equivalent to how many dollars?
1p+28c = (5/3)d + 28* (4/21) d = (5/3) d + (16/3) d = (21/3) d = 7 d
Answer : A
