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A purse contains 57 coins, all of which are nickels, dimes, or quarter
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gmatt1476
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A purse contains 57 coins, all of which are nickels, dimes, or quarter [#permalink] New post  27 Apr 2020, 12:20
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A purse contains 57 coins, all of which are nickels, dimes, or quarters. If the purse contains x dimes and 8 more nickels than dimes, which of the following gives the number of quarters the purse contains in terms of x ?

A. 2x − 49
B. 2x + 49
C. 2x − 65
D. 49 − 2x
E. 65 − 2x


PS25440.02
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subhakimi
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Re: A purse contains 57 coins, all of which are nickels, dimes, or quarter [#permalink] New post  27 Apr 2020, 12:28
Bunuel wrote:
A purse contains 57 coins, all of which are nickels, dimes, or quarters. If the purse contains x dimes and 8 more nickels than dimes, which of the following gives the number of quarters the purse contains in terms of x ?

A. 2x − 49
B. 2x + 49
C. 2x − 65
D. 49 − 2x
E. 65 − 2x


PS25440.02


Dimes = X
Nickle = X + 8
Quarters = 57 - x - (x + 8) = 49 - 2X

Trick -
Total were 57
Nickel 8 more than something it means without those 8 we are left with 49 so answer has to be in the format 49 - Something. Only one option even without solving.
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nick1816
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Re: A purse contains 57 coins, all of which are nickels, dimes, or quarter [#permalink] New post  27 Apr 2020, 12:32
Dimes = x

Nickels = x+8

Quarters = y

x+x+8+y = 57

y= 49-2x

gmatt1476 wrote:
A purse contains 57 coins, all of which are nickels, dimes, or quarters. If the purse contains x dimes and 8 more nickels than dimes, which of the following gives the number of quarters the purse contains in terms of x ?

A. 2x − 49
B. 2x + 49
C. 2x − 65
D. 49 − 2x
E. 65 − 2x


PS25440.02
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BrentGMATPrepNow
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Re: A purse contains 57 coins, all of which are nickels, dimes, or quarter [#permalink] New post  27 Apr 2020, 17:27
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gmatt1476 wrote:
A purse contains 57 coins, all of which are nickels, dimes, or quarters. If the purse contains x dimes and 8 more nickels than dimes, which of the following gives the number of quarters the purse contains in terms of x ?

A. 2x − 49
B. 2x + 49
C. 2x − 65
D. 49 − 2x
E. 65 − 2x


PS25440.02


Given: x = the number of dimes

The purse contains 8 more nickels than dimes
So, x + 8 = the number of nickels


The purse contains 57 coins
In other words: (number of nickels) + (number of dimes) + (number of quarters) = 57
Substitute to get: (x + 8) + x + (number of quarters) = 57
Simplify: 2x + 8 + (number of quarters) = 57


Which of the following gives the number of quarters the purse contains in terms of x ?
Take: 2x + 8 + (number of quarters) = 57
Subtract 8 from both sides of the equation to get: 2x + (number of quarters) = 49
Subtract 2x from both sides to get: number of quarters = 49 - 2x

Answer: D

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Brent
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Re: A purse contains 57 coins, all of which are nickels, dimes, or quarter [#permalink] New post  21 Dec 2020, 04:08
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gmatt1476 wrote:
A purse contains 57 coins, all of which are nickels, dimes, or quarters. If the purse contains x dimes and 8 more nickels than dimes, which of the following gives the number of quarters the purse contains in terms of x ?

A. 2x − 49
B. 2x + 49
C. 2x − 65
D. 49 − 2x
E. 65 − 2x


Dimes \(= x\)

Nickle \(= x + 8\)

Quarters \(= 57 - x - (x + 8)\)

\(= 49 - 2x\)

The answer is \(D\)
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