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# Darion has at least one quarter, one dime, one nickel, and o

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Darion has at least one quarter, one dime, one nickel, and o [#permalink]  29 Jul 2020, 10:37
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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
[Reveal] Spoiler: OA

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Re: Darion has at least one quarter, one dime, one nickel, and o [#permalink]  29 Jul 2020, 11:41
Let us denote # of pennies as P, dimes as D, nickels as N, and quarters as Q.
three times as many dimes as quarters => D = 3Q
three times as many nickels as dimes => N = 3D = 9Q
three times as many pennies as nickels => P = 3N = 27Q
total number of coins = Q + 3Q + 9Q + 27Q = 40Q
=> 120 = 40Q
=> Q = 3

money in quarters = 3/4 = 0.75
money in dimes = 9/10 = 0.9
money in nickels = 27/20 = 1.35
money in pennies = 81/100 = 0.81
total money = 3.81

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Re: Darion has at least one quarter, one dime, one nickel, and o [#permalink]  03 Aug 2020, 05:19
Expert's post
Carcass wrote:
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

NOTE: The official test-makers will not assume that you know the values of quarters, nickels, dimes and pennies.
1 quarter = \$0.25
1 dime = \$0.10
1 nickel = \$0.05
1 penny = \$0.01

Let's start with the smallest value, which happens to be the number of quarters

Let x = the number of quarters in Darion's pocket

He has three times as many dimes as quarters
So, 3x = the number of dimes

He has three times as many nickels as dimes
So, 3(3x) = the number of nickels
In other words, 9x) = the number of nickels

He has three times as many pennies as nickels
So, 3(9x) = the number of pennies
In other words, 27x) = the number of pennies

He has 120 coins
In other words: (number of quarters) + (number of dimes) + (number of nickels) + (number of pennies) = 120
Substitute to get: x + 3x + 9x + 27x = 120
Simplify: 40x = 120
Solve: x = 3

When we plug x = 3 into all of the above expressions, we find that there are:
3 quarters (\$0.75)
9 dimes (\$0.90)
27 nickels (\$1.35)
81 pennies (\$0.81)

How much money does he have?
\$0.75 + \$0.90 + \$1.35 + \$0.81 = \$3.81

Cheers,
Brent
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Re: Darion has at least one quarter, one dime, one nickel, and o [#permalink]  11 Aug 2020, 05:09
GreenlightTestPrep wrote:
Carcass wrote:
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

NOTE: The official test-makers will not assume that you know the values of quarters, nickels, dimes and pennies.
1 quarter = \$0.25
1 dime = \$0.10
1 nickel = \$0.05
1 penny = \$0.01

Let's start with the smallest value, which happens to be the number of quarters

Let x = the number of quarters in Darion's pocket

He has three times as many dimes as quarters
So, 3x = the number of dimes

He has three times as many nickels as dimes
So, 3(3x) = the number of nickels
In other words, 9x) = the number of nickels

He has three times as many pennies as nickels
So, 3(9x) = the number of pennies
In other words, 27x) = the number of pennies

He has 120 coins
In other words: (number of quarters) + (number of dimes) + (number of nickels) + (number of pennies) = 120
Substitute to get: x + 3x + 9x + 27x = 120
Simplify: 40x = 120
Solve: x = 3

When we plug x = 3 into all of the above expressions, we find that there are:
3 quarters (\$0.75)
9 dimes (\$0.90)
27 nickels (\$1.35)
81 pennies (\$0.81)

How much money does he have?
\$0.75 + \$0.90 + \$1.35 + \$0.81 = \$3.81

Cheers,
Brent

Will the value of quarter,dime nickel and penny be given in the official test?
Re: Darion has at least one quarter, one dime, one nickel, and o   [#permalink] 11 Aug 2020, 05:09
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# Darion has at least one quarter, one dime, one nickel, and o

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