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# A certain purse contains 30 coins, Each coin is either a nickel or

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Intern
Joined: 05 Sep 2013
Posts: 9
Location: Georgia
A certain purse contains 30 coins, Each coin is either a nickel or  [#permalink]

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Updated on: 17 Nov 2014, 10:37
1
3
00:00

Difficulty:

35% (medium)

Question Stats:

66% (01:53) correct 34% (02:09) wrong based on 81 sessions

A certain purse contains 30 coins, Each coin is either a nickel or a quarter. If the total value of all coins in the purse is 4.70$, how many nickels does the purse contain? A. 12 B. 14 C. 16 D. 20 E. 22 Originally posted by NATABERI on 17 Nov 2014, 03:24. Last edited by Bunuel on 17 Nov 2014, 10:37, edited 1 time in total. Edited the question. Manager Joined: 21 Jul 2014 Posts: 126 Re: A certain purse contains 30 coins, Each coin is either a nickel or [#permalink] ### Show Tags 17 Nov 2014, 07:23 1 NATABERI wrote: A certain purse contains 30 coins, Each coin is either a nickel or a quarter. If the total value of all coins in the purse is 4.70$, how many nickels does the purse contain?

To frame this as an equation:

n = number of nickels
q = number of quarters

1) $$.25q + .05n = 4.7$$
2) $$q + n = 30$$

So now you just need to solve for n.

$$q + n = 30$$
$$q = 30 - n$$

$$.25q + .05n = 4.7$$
$$.25(30-n) + .05n = 4.7$$
$$7.5 - .25n + .05n = 4.7$$
$$7.5 - .2n = 4.7$$
$$7.5 = 4.7 + .2n$$
$$7.5 - 4.7 = .2n$$
$$2.8 = .2n$$
$$2.8/.2 = n$$
$$14 = n$$

There are 14 nickels in the purse.
Manager
Joined: 10 Sep 2014
Posts: 97
Re: A certain purse contains 30 coins, Each coin is either a nickel or  [#permalink]

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17 Nov 2014, 08:57
1
I picked a starting point and then kept ballparking until i hit the right answer

$4.70 - 6 quarters =$3.20. this would be 6 quarters and 64 nickels, WAY more than 30 so we need a lot more quarters

$4.70 - 16 quarters =$0.70 this would be 16 quarters and 14 nickels, 30 coins!

14 nickels!
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Re: A certain purse contains 30 coins, Each coin is either a nickel or  [#permalink]

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20 Nov 2014, 22:57
Nickels ......................... Quarters ................ Total

0.05 ................................. 0.25 ................... 4.70 (Total Value)

x ................................... (30-x) ..................... 30 (Quantity)

Setting up the equation

0.05x + 0.25 (30-x) = 4.70

5x + 25(30-x) = 470

x + 5(30-x) = 94

x = 14

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Re: A certain purse contains 30 coins, Each coin is either a nickel or  [#permalink]

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15 Dec 2017, 15:30
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Top Contributor
NATABERI wrote:
A certain purse contains 30 coins, Each coin is either a nickel or a quarter. If the total value of all coins in the purse is 4.70$, how many nickels does the purse contain? A. 12 B. 14 C. 16 D. 20 E. 22 ASIDE: Each nickel is worth 5 cents ($0.05) and each quarter is worth 25 cents ($0.25) Let n = the number of nickels in the purse This means (30-n) = the number of quarters in the purse (since there is a total of 30 COINS) Since each nickel is worth 5 cents, we know that n nickels is worth 5n CENTS Likewise, since each quarter is worth 25 cents, we know that (30-n) quarters is worth 25(30-n) CENTS The total value of all coins in the purse is$ 4.70
We can also say that the TOTAL value is 470 CENTS
So, we can write: (value of all nickels) + (value of all quarters) = 470 CENTS
Or: 5n + 25(30-n) = 470
Expand: 5n + 750 - 25n = 470
Simplify: -20n + 750 = 470
Subtract 750 from both sides: -20n = -280
Solve: n = 14

Cheers,
Brent
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Intern
Joined: 08 Dec 2017
Posts: 17
Re: A certain purse contains 30 coins, Each coin is either a nickel or  [#permalink]

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15 Dec 2017, 18:22
The average value of a coin is 4.70/30 =.157
So about 16 cents. That is 11 cents more than a nickel and 9 cents less than a quarter. If there were an equal numbers of quarters and nickels the average would come out to 15 cents a coin. There there are slightly more quarters than nickels. 14 is the only viable answer.

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Re: A certain purse contains 30 coins, Each coin is either a nickel or &nbs [#permalink] 15 Dec 2017, 18:22
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