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09 Oct 2020, 04:00
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
71% (02:59) correct
29%
(03:04)
wrong
based on 254
sessions
History
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Darion has at least one quarter, one dime, one nickel, and one penny in his pocket. He has three times as many pennies as nickels, three times as many nickels as dimes, and three times as many dimes as quarters. If he has 120 coins, how much money does he have?
A. $1.20
B. $3.81
C. $4.06
D. $4.07
E. $7.75
A. $1.20
B. $3.81
C. $4.06
D. $4.07
E. $7.75
09 Oct 2020, 09:15
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Darion has at least one quarter, one dime, one nickel, and one penny in his pocket. He has three times as many pennies as nickels, three times as many nickels as dimes, and three times as many dimes as quarters. If he has 120 coins, how much money does he have?
A. $1.20
B. $3.81
C. $4.06
D. $4.07
E. $7.75
Explanation:
let us assume that Darion has Q quarters, D dimes, N nickels, and P pennies
then given P=3N, N=3D, D=3Q and also given
P+N+D+Q=120
i.e 27Q+9Q+3Q+Q=120
Q=3
means P=81, N=27, D=9 (as P=3N, N=3D, D=3Q)
also we know that one penny=1 cent, one nickel=5 cent ,one dime=10 cent, one quarter=25 cent
So overall money =81*1 + 27*5 + 9*10 + 3*25
=381 cents OR $3.81
Hence B is the correct answer.
A. $1.20
B. $3.81
C. $4.06
D. $4.07
E. $7.75
Explanation:
let us assume that Darion has Q quarters, D dimes, N nickels, and P pennies
then given P=3N, N=3D, D=3Q and also given
P+N+D+Q=120
i.e 27Q+9Q+3Q+Q=120
Q=3
means P=81, N=27, D=9 (as P=3N, N=3D, D=3Q)
also we know that one penny=1 cent, one nickel=5 cent ,one dime=10 cent, one quarter=25 cent
So overall money =81*1 + 27*5 + 9*10 + 3*25
=381 cents OR $3.81
Hence B is the correct answer.
09 Oct 2020, 10:29
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If he had 1 quarter, he'd have 3 dimes, 9 nickels and 27 pennies. So he has coins in a 1 to 3 to 9 to 27 ratio. Those four numbers sum to 40, but he actually has 120 coins in total, which is (3)(40), so he must have 3 quarters, 9 dimes, 27 nickels and 81 pennies. He clearly has more than $1.20 in total, and when we compute the total amount of money he has, the result in cents must be a multiple of 3 (because the number of coins of each type is a multiple of 3). Summing the digits of each answer choice from B through E, only B can be right.
