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Total value of 5 cent coins

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by gmattesttaker2 » Sat Nov 02, 2013 1:33 pm
Hello,

Can you please assist with this:

Pedro has some coins in his pocket, some are 5-cent coins and some are 25-cent coins. If the average value of each coin in Pedro's pocket is 10 cents and he has $8 in his pocket, what is the total value of his 5-cent coins?

Ans: [spoiler]$6[/spoiler]

My approach was as follows:

10 = (Sum of all 5 cent coins)(number of 5 cent coins) + ( Sum of all 25 cent coins)(number of 25 cent coins)/(number of 5 cent coins + number of 25 cent coins)

=> (Sum of all 5 cent coins)(number of 5 cent coins) + ( Sum of all 25 cent coins)(number of 25 cent coins) = 10 (number of 5 cent coins + number of 25 cent coins)

Given, (Sum of all 5 cent coins)(number of 5 cent coins) + ( Sum of all 25 cent coins)(number of 25 cent coins) = 800

So, 10 (number of 5 cent coins + number of 25 cent coins) = 800

=> (number of 5 cent coins + number of 25 cent coins) = 80

However, I am stuck here. Can you please assist?


Thanks a lot for your help - Sri
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by Brent@GMATPrepNow » Sat Nov 02, 2013 1:54 pm
gmattesttaker2 wrote:
Pedro has some coins in his pocket, some are 5-cent coins and some are 25-cent coins. If the average value of each coin in Pedro's pocket is 10 cents and he has $8 in his pocket, what is the total value of his 5-cent coins?
This is a good start, Sri, but adding some variables will help A LOT.

Let F = number of five-cent coins
Let T = number of twenty-five-cent coins

IMPORTANT:
If I have 3 five-cents coins, then I have a total of (3)(5) cents [aka 15 cents]
If I have 11 five-cents coins, then I have a total of (11)(5) cents [aka 55 cents]
So, if I have F five-cents coins, then I have a total of 5F cents
Likewise, if I have T twenty-five-cents coins, then I have a total of 25T cents

Pedro has $8 in his pocket
In other words, Pedro has 800 cents.
So, we can write 5F + 25T = 800

The average value of each coin in Pedro's pocket is 10 cents
Average = (total value)/(total number of coins)
So, 10 cents = (800)/(total number of coins)
We can conclude that there are 80 coins altogether
So, we can write F + T = 80

We now have this system . . .
5F + 25T = 800
F + T = 80
. . . that we can solve for F (and T)

When we do so, we get F = 60 and T = 20
If Pedro has 60 five-cent coins then the total value of his five-cent coins is [spoiler]$3[/spoiler]

Cheers,
Brent
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by gmattesttaker2 » Sat Nov 02, 2013 2:33 pm
Brent@GMATPrepNow wrote:
gmattesttaker2 wrote:
Pedro has some coins in his pocket, some are 5-cent coins and some are 25-cent coins. If the average value of each coin in Pedro's pocket is 10 cents and he has $8 in his pocket, what is the total value of his 5-cent coins?
This is a good start, Sri, but adding some variables will help A LOT.

Let F = number of five-cent coins
Let T = number of twenty-five-cent coins

IMPORTANT:
If I have 3 five-cents coins, then I have a total of (3)(5) cents [aka 15 cents]
If I have 11 five-cents coins, then I have a total of (11)(5) cents [aka 55 cents]
So, if I have F five-cents coins, then I have a total of 5F cents
Likewise, if I have T twenty-five-cents coins, then I have a total of 25T cents

Pedro has $8 in his pocket
In other words, Pedro has 800 cents.
So, we can write 5F + 25T = 800

The average value of each coin in Pedro's pocket is 10 cents
Average = (total value)/(total number of coins)
So, 10 cents = (800)/(total number of coins)
We can conclude that there are 80 coins altogether
So, we can write F + T = 80

We now have this system . . .
5F + 25T = 800
F + T = 80
. . . that we can solve for F (and T)

When we do so, we get F = 60 and T = 20
If Pedro has 60 five-cent coins then the total value of his five-cent coins is [spoiler]$3[/spoiler]

Cheers,
Brent
Hello Brent,

Thank you very much for your detailed and excellent (as always) explanation. It is clear now. Many thanks again for all your help.

Best Regards,
Sri
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by gmattesttaker2 » Sat Feb 08, 2014 6:27 pm
Brent@GMATPrepNow wrote:
gmattesttaker2 wrote:
Pedro has some coins in his pocket, some are 5-cent coins and some are 25-cent coins. If the average value of each coin in Pedro's pocket is 10 cents and he has $8 in his pocket, what is the total value of his 5-cent coins?
This is a good start, Sri, but adding some variables will help A LOT.

Let F = number of five-cent coins
Let T = number of twenty-five-cent coins

IMPORTANT:
If I have 3 five-cents coins, then I have a total of (3)(5) cents [aka 15 cents]
If I have 11 five-cents coins, then I have a total of (11)(5) cents [aka 55 cents]
So, if I have F five-cents coins, then I have a total of 5F cents
Likewise, if I have T twenty-five-cents coins, then I have a total of 25T cents

Pedro has $8 in his pocket
In other words, Pedro has 800 cents.
So, we can write 5F + 25T = 800

The average value of each coin in Pedro's pocket is 10 cents
Average = (total value)/(total number of coins)
So, 10 cents = (800)/(total number of coins)
We can conclude that there are 80 coins altogether
So, we can write F + T = 80

We now have this system . . .
5F + 25T = 800
F + T = 80
. . . that we can solve for F (and T)

When we do so, we get F = 60 and T = 20
If Pedro has 60 five-cent coins then the total value of his five-cent coins is [spoiler]$3[/spoiler]

Cheers,
Brent

Hello Brent,

The official explanation says the following:

The distance from the nickels (the 5-cent coins) to the average is 5, and the distance from the quarters (the 25-cent coins) to the average is 15, so the ratio is N/Q = 15/5 = 3/1. Now we set our ratios problem and 3x + x = 8x, so x = 2 and since we got 3 parts of nickels 3(2) = $6.

I was just wondering where the OA is going wrong here? Thanks a lot for your help.

Best Regards,
Sri
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by Brent@GMATPrepNow » Sat Feb 08, 2014 6:41 pm
The answer in this resource is that there are $6 in nickels? This would give us $2 in quarters.

$6 in nickels = 120 nickels.
$2 in quarters = 8 quarters.

Total # of coins = 128
Total value of coins = $8 = 800 cents

So, average value of each coin = 800/128
= 6.25 cents BUT the question says that the average value of each coin is 10 cents.

So, the answer key in that resource is incorrect. What's the source of this question?

Cheers,
Brent
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by gmattesttaker2 » Sat Feb 08, 2014 6:51 pm
Brent@GMATPrepNow wrote:The answer in this resource is that there are $6 in nickels? This would give us $2 in quarters.

$6 in nickels = 120 nickels.
$2 in quarters = 8 quarters.

Total # of coins = 128
Total value of coins = $8 = 800 cents

So, average value of each coin = 800/128
= 6.25 cents BUT the question says that the average value of each coin is 10 cents.

So, the answer key in that resource is incorrect. What's the source of this question?

Cheers,
Brent
Hello Brent,

Thank you very much for your prompt response and for your clear explanation. This question is from a GMAT word problems book that I purchased online. I will be careful with the explanations given in the book since obviously it has some mistakes here. Thanks for all your help.

Best Regards,
Sri
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