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Andrew has a certain number of coins in his pocket. He has

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Andrew has a certain number of coins in his pocket. He has

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Andrew has a certain number of coins in his pocket. He has three times as many dimes as quarters and six times as many nickels as dimes. A nickel is worth $0.05, a dime is worth $0.10 and a quarter is worth $0.25. If he has a total of $10.15, then which of the following represents the number of dimes in Andrew’s pocket?

A. 9
B. 10
C. 18
D. 20
E. 21

The OA is E.

Source: EMPOWERgmat

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swerve wrote:
Andrew has a certain number of coins in his pocket. He has three times as many dimes as quarters and six times as many nickels as dimes. A nickel is worth $0.05, a dime is worth $0.10 and a quarter is worth $0.25. If he has a total of $10.15, then which of the following represents the number of dimes in Andrew’s pocket?

A. 9
B. 10
C. 18
D. 20
E. 21
Let x = number of QUARTERS in pocket
So, 0.25x = VALUE of quarters in pocket

He has three times as many dimes as quarters
So, 3x = number of DIMES in pocket
So, 0.10(3x) = 0.3x = VALUE of dimes in pocket

He has six times as many nickels as dimes.
So, (6)(3x) = number of NICKELS in pocket
In other words, 18x = number of NICKELS in pocket
So, 0.05(18x) = 0.9x = VALUE of nickels in pocket

He has a total of $10.15
So: 0.25x + 0.3x +0.9x = $10.15
Simplify: 1.45x = $10.15
Solve: x = 10.15/1.45 = 7

So there are 7 QUARTERS, 21 DIMES and 126 NICKELS

Answer: E

Cheers,
Brent

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