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# The average value of all the pennies, nickels, dimes,

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Senior Manager
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Joined: 02 Nov 2018
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The average value of all the pennies, nickels, dimes,  [#permalink]

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11 Mar 2019, 00:36
00:00

Difficulty:

45% (medium)

Question Stats:

50% (01:03) correct 50% (02:55) wrong based on 14 sessions

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The average value of all the pennies, nickels, dimes, and quarters in Paula’s purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse?

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4
Senior Manager
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Joined: 02 Nov 2018
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The average value of all the pennies, nickels, dimes,  [#permalink]

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16 Mar 2019, 10:16
1
hi stne

If the new coin was worth 20 cents, adding it would not change the mean.
The additional 5 cents raise the mean by 1, thus the new number of coins must be 5.
Therefore there were 4 coins worth a total of 4X20=80 cents. only way to get 80 cents using 4 coins is 25+25+25+5.
Thus, having three quarters, one nickel, and no dimes
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Joined: 27 May 2012
Posts: 952
Re: The average value of all the pennies, nickels, dimes,  [#permalink]

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16 Mar 2019, 10:48
1
hi stne

If the new coin was worth 20 cents, adding it would not change the mean.
The additional 5 cents raise the mean by 1, thus the new number of coins must be 5.
Therefore there were 4 coins worth a total of 4X20=80 cents. only way to get 80 cents using 4 coins is 25+25+25+5.
Thus, having three quarters, one nickel, and no dimes

Thank you, but really not able to understand the solution.
Can you help me with the algebraic solution , I tried this way:

$$\frac{1P +5N+10D+25Q}{P+N+D+Q}=20$$ (I)

$$\frac{1P +5N+10D+25(Q+1)}{P+N+D+Q}=21$$ (II)

solving I we get 5Q=19P+15N+10D
solving II we get 4Q+25=20P+16N+11D

II-I ( Subtracting I from II) -Q+25=P+N+D or P+N+D+Q =25

After this, how do we deduce the solution?
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- Stne
Senior Manager
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Joined: 02 Nov 2018
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The average value of all the pennies, nickels, dimes,  [#permalink]

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Updated on: 16 Mar 2019, 11:28
2
hi @
ur way is too complex and time consuming .
if u want algebraic way do this way
Let the total value, in cents, of the coins Paula has originally be v
and the number of coins she has be n
so, v/n = 20
v= 20n
and ,
v+25/n+1=21
Substituting yields: 20n+25=21(n+1),
so n=4 thats mean total number of coin = 4
so v= 20x4
v= 80 cents
Then, we see that the only way Paula can satisfy this rule is if she had 3 quarters and 1 nickel in her purse.(3X25+5)
so no dimes

Originally posted by Noshad on 16 Mar 2019, 11:13.
Last edited by Noshad on 16 Mar 2019, 11:28, edited 1 time in total.
Director
Joined: 27 May 2012
Posts: 952
Re: The average value of all the pennies, nickels, dimes,  [#permalink]

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16 Mar 2019, 11:22
hi @
ur way is too complex and time consuming .
if u want algebraic way do this way
Let the total value, in cents, of the coins Paula has originally be v
and the number of coins she has be n
so, v/n = 20
v= 20n
and ,
v+25/n+1=21
Substituting yields: 20n+25=21(n+1),
so n=4 thats mean total number of coin = 4
so v= 20x4
v= 80 cents
Then, we see that the only way Paula can satisfy this rule is if she had 3 quarters and 1 nickel in her purse.(3X20+10)
so no dimes

Thank you +1, great solution. But there is small typo at the end , you may wish to edit (3X20+10) to (3*25 +5). Thanks.
_________________
- Stne
Re: The average value of all the pennies, nickels, dimes,   [#permalink] 16 Mar 2019, 11:22
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# The average value of all the pennies, nickels, dimes,

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