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Ian regularly empties his pockets of coins into a jar. One day, he co
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04 Aug 2022, 03:06
04 Aug 2022, 03:06
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Question Stats:
50% (02:44) correct
50% (03:26) wrong based on 6 sessions
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Ian regularly empties his pockets of coins into a jar. One day, he counts the money and finds that he has $22.50 in nickels (worth 5 cents each), dimes (each worth 10 cents), and quarters (each worth 25 cents.) He has 3 times as many nickels as dimes, and 6 more quarters than dimes. How much money does he have in quarters?
A $11.25
B $12.00
C $15.50
D $19.75
E $20.50
A $11.25
B $12.00
C $15.50
D $19.75
E $20.50
Show: ::
nickels and dimes
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
Re: Ian regularly empties his pockets of coins into a jar. One day, he co
[#permalink]
22 Aug 2022, 10:58
22 Aug 2022, 10:58
Expert Reply
OE
Quote:
Explanation: let n = # of nickels, d = # of dimes, and q = # of quarters.
Then, n = 3d and q = d+6. Each nickel is worth 0.05 dollars, each dime
0.10, and each quarter 0.25, and it all has to add up to $22.50. So (0.05)n
+ (0.10)d + (0.25)q = 22.50. Multiply through by 100 to clear the
decimals, to get 5n + 10d + 25q = 2250. Now, put everything in terms of
d: 5(3d) + 10d + 25(d+6) = 2250. Multiply through: 15d + 10d + 25d
+150 = 2250. Combine like terms and solve for d: 50d =2100, so d = 42.
Then n = 3d = 126 and q = 48. The value of 48 quarters is 48(0.25) =
$12.00.
Then, n = 3d and q = d+6. Each nickel is worth 0.05 dollars, each dime
0.10, and each quarter 0.25, and it all has to add up to $22.50. So (0.05)n
+ (0.10)d + (0.25)q = 22.50. Multiply through by 100 to clear the
decimals, to get 5n + 10d + 25q = 2250. Now, put everything in terms of
d: 5(3d) + 10d + 25(d+6) = 2250. Multiply through: 15d + 10d + 25d
+150 = 2250. Combine like terms and solve for d: 50d =2100, so d = 42.
Then n = 3d = 126 and q = 48. The value of 48 quarters is 48(0.25) =
$12.00.
gmatclubot
Re: Ian regularly empties his pockets of coins into a jar. One day, he co [#permalink]
22 Aug 2022, 10:58
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