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Cathy has equal numbers of nickels

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by BTGmoderatorDC » Fri Dec 08, 2017 10:24 pm
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

I am confused about the best solution to get the answer in this, can some experts help?

OA C
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by GMATGuruNY » Sat Dec 09, 2017 3:28 am
lheiannie07 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
Since Cathy has an equal number of nickels and quarters:
Let x = the number of each coin.
Since each nickel is worth 5 cents, the total value of the x nickels = 5x.
Since each quarter is worth 25 cents, the total value of the x quarters = 25x.
Since the total amount of money is $7.50 -- the equivalent of 750 cents -- we get:
5x + 25x = 750
30x = 750
3x = 75
x = 25.

Since Cathy has 25 nickels and 25 quarters, the total number of coins = 25 + 25 = 50.

The correct answer is C.
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by Brent@GMATPrepNow » Sat Dec 09, 2017 7:34 am
lheiannie07 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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by [email protected] » Sat Dec 09, 2017 2:29 pm
Hi lheiannie07,

We're told that Cathy has EQUAL numbers of nickels and quarters worth a total of $7.50. We're asked for the TOTAL number of coins that she has. (nickel = 5 cents, quarter = 25 cents).

Since there are an EQUAL number of coins, one nickel + one quarter = 5+25 = 30 cents. Thus, that $7.50 is made up of 'groups' of 30 cents...

750/30 = 25 groups of 2 coins each
25 nickels and 25 quarters = 50 total coins

Final Answer: C

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by Scott@TargetTestPrep » Sun Sep 29, 2019 6:01 pm
BTGmoderatorDC 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

I am confused about the best solution to get the answer in this, can some experts help?

OA C
We can create the equation:

0.05n + 0.25n = 7.5

5n + 25n = 750

30n = 750

n = 25

So, she has a total of 25 + 25 = 50 coins.

Answer: C

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