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Cathy has equal numbers of nickels and quarters worth a total of $7.50

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Cathy has equal numbers of nickels and quarters worth a total of $7.50 [#permalink]

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New post 28 May 2017, 02:35
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Cathy has equal numbers of nickels and quarters worth a total of $7.50. How many coins does she have?
(nickel = 5 cents, quarter = 25 cents)

(A) 20
(B) 25
(C) 50
(D) 62
(E) 70
[Reveal] Spoiler: OA

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Re: Cathy has equal numbers of nickels and quarters worth a total of $7.50 [#permalink]

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New post 28 May 2017, 02:42
we know that the value of quarters should be higher than half ..by number crunching if we have 25 coins of each ( 25 cents making 6.25 $ and 25 nickels making 1.25 $ ) total is 7.50$ hence total coins would be 50 option C


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Cathy has equal numbers of nickels and quarters worth a total of $7.50 [#permalink]

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New post 28 May 2017, 10:16
Bunuel wrote:
Cathy has equal numbers of nickels and quarters worth a total of $7.50. How many coins does she have?
(nickel = 5 cents, quarter = 25 cents)

(A) 20
(B) 25
(C) 50
(D) 62
(E) 70

Number of nickels and quarters is equal, so

Let C = 1/2 of total number of coins

(Equal #s of coins times different values of coins, then summed, given a total of $7.50, will yield # of coins)

.05C + .25C = 7.50 ==>

5C + 25C = 750

30 C = 750, and

C = 25

TOTAL coins? C = 1/2 of total, so 2C = 50 coins total
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Re: Cathy has equal numbers of nickels and quarters worth a total of $7.50 [#permalink]

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New post 28 May 2017, 10:41
Bunuel wrote:
Cathy has equal numbers of nickels and quarters worth a total of $7.50. How many coins does she have?
(nickel = 5 cents, quarter = 25 cents)

(A) 20
(B) 25
(C) 50
(D) 62
(E) 70


\(\frac{5}{100}*n + \frac{25}{100}n = 7.50\)

Or, \(30n = 750\)

Or, n = 25

So, Total number of coins with Cathy is 25*2 = 50 coins...

Thus, answer must be (C) 50
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Re: Cathy has equal numbers of nickels and quarters worth a total of $7.50 [#permalink]

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New post 29 May 2017, 02:44
5x + 25 X = 750
30 x = 750
x= 25,,

total number of coins = 25 + 25 = 50.. ans C

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Re: Cathy has equal numbers of nickels and quarters worth a total of $7.50 [#permalink]

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New post 09 Dec 2017, 07:33
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Bunuel wrote:
Cathy has equal numbers of nickels and quarters worth a total of $7.50. How many coins does she have?
(nickel = 5 cents, quarter = 25 cents)

(A) 20
(B) 25
(C) 50
(D) 62
(E) 70


Another approach is the test the answer choices.
When doing so, it's best to start with the middlemost answer choice.

C) 50
If there are 50 coins in total, and half are nickels and half are quarters, then we have 25 nickels and 25 quarters.
25 nickels is worth $1.25 (since 25 x $0.05 = $1.25)
25 quarters is worth $6.25 (since 25 x $0.65 = $6.25)
TOTAL value = #1.25 + $6.25 = $7.50 (PERFECT!)\

Answer: C

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Re: Cathy has equal numbers of nickels and quarters worth a total of $7.50   [#permalink] 09 Dec 2017, 07:33
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