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Penniless Pete's piggy bank has no pennies in it, but it has 100 coins

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Penniless Pete's piggy bank has no pennies in it, but it has 100 coins  [#permalink]

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New post 20 Mar 2019, 06:12
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Question Stats:

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Penniless Pete's piggy bank has no pennies in it, but it has 100 coins, all nickels,dimes, and quarters, whose total value is $8.35. It does not necessarily contain coins of all three types. What is the difference between the largest and smallest number of dimes that could be in the bank? (Dime= 10 cents; Nickel= 5 cents; Penny= 1 cent)

(A) 0
(B) 13
(C) 37
(D) 64
(E) 83

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Re: Penniless Pete's piggy bank has no pennies in it, but it has 100 coins  [#permalink]

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New post 20 Mar 2019, 06:38
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Bunuel wrote:
Penniless Pete's piggy bank has no pennies in it, but it has 100 coins, all nickels,dimes, and quarters, whose total value is $8.35. It does not necessarily contain coins of all three types. What is the difference between the largest and smallest number of dimes that could be in the bank? (Dime= 10 cents; Nickel= 5 cents; Penny= 1 cent)

(A) 0
(B) 13
(C) 37
(D) 64
(E) 83


Let d,n and q be the number of dime,nickel and quarter respectively.

0.05n+0.1d+0.25q=8.35
=> 5n + 10d + 25q = 835
=> n + 2d + 5q = 167.....1)

and

n+d+q=100.....2)

Subtracting 2) from 1

d + 4q = 67

The equation will have max d when d=67 and q=0 (since it is not necessary for the piggy bank to contain all the three type of coins)
The equation will have min value when d=3 and q=16.

Difference between largest and smallest number of dime = 67 - 3=64. (D)
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Re: Penniless Pete's piggy bank has no pennies in it, but it has 100 coins  [#permalink]

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New post 20 Mar 2019, 07:51
Bunuel wrote:
Penniless Pete's piggy bank has no pennies in it, but it has 100 coins, all nickels,dimes, and quarters, whose total value is $8.35. It does not necessarily contain coins of all three types. What is the difference between the largest and smallest number of dimes that could be in the bank? (Dime= 10 cents; Nickel= 5 cents; Penny= 1 cent)

(A) 0
(B) 13
(C) 37
(D) 64
(E) 83


a+b+c=100--1
and
.1a+.05b+.25c = 8.35
or say
10a+5b+25c= 835
2a+b+5c=167 --2
subtract 2 from 1
a+4c=67
c = 16 , a =3
or 67 of dimes and 0 quarters
so difference 67-3 ; 64
IMO D
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Re: Penniless Pete's piggy bank has no pennies in it, but it has 100 coins  [#permalink]

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New post 22 Mar 2019, 09:26
Bunuel wrote:
Penniless Pete's piggy bank has no pennies in it, but it has 100 coins, all nickels,dimes, and quarters, whose total value is $8.35. It does not necessarily contain coins of all three types. What is the difference between the largest and smallest number of dimes that could be in the bank? (Dime= 10 cents; Nickel= 5 cents; Penny= 1 cent)

(A) 0
(B) 13
(C) 37
(D) 64
(E) 83


Let n, d, and q be the number of nickels, dimes, and quarters, respectively. We can generate two equations:

n + d + q = 100 (Number of coins equation)

and

5n + 10d + 25q = 835 (Money value equation, in cents)

n + 2d + 5q = 167

Subtracting the first equation from the second, we have:

d + 4q = 67

To maximize the number of dimes, we minimize the number of quarters. If we have no quarters (q = 0), we will have 67 dimes, and this is the maximum number of dimes.

Now, to minimize the number of dimes, we must maximize the number of quarters. So 4q must be as large as possible, and this occurs when q = 16. When q = 16, then d = 3. Thus, the minimum number of dimes is 3.

The difference between the maximum and minimum number of dimes is 67 - 3 = 64.

Answer: D
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Re: Penniless Pete's piggy bank has no pennies in it, but it has 100 coins   [#permalink] 22 Mar 2019, 09:26
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