A certain purse contains 30 coins, Each coin is either a...

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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

The OA is B.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

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by Brent@GMATPrepNow » Fri Dec 15, 2017 3:30 pm
LUANDATO 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

The OA is B.
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

Answer: B

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by [email protected] » Fri Dec 15, 2017 3:33 pm
Hi LUANDATO,

We're told that a purse contains 30 coins, each coin is either a nickel (worth $0.05 each) or a quarter (worth $0.25 each) and the total value of all coins in the purse is $4.70. We're asked for the number of nickels in the purse. This question can be solved in a couple of different ways (including a 'system' of Algebraic equations). However, there is a great 'shortcut' in this question that can help you avoid a lot of that 'math' and focus on the answer choices.

The total value of the QUARTERS in the purchase can only "end" in a few possibilities: .00, .25, .50 or .75. Since the total of ALL the coins is $4.70, the 20 cents above $4.50 can ONLY be from the value of 4 nickels. Thus, the number of nickels is going to be 4 greater than some 'round number' (meaning a multiple of 5 or 10). Let's TEST Answer B...

IF... there are 14 nickels....
14 nickels --> (14)($.05) = $0.70
30 total coins means 16 quarters --> (16)($0.25) = $4.00
$0.70 + $4.00 = $4.70
This is an exact match for what we were told, so this MUST be the answer.

Final Answer: B

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by Scott@TargetTestPrep » Mon Sep 23, 2019 4:37 pm
BTGmoderatorLU 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

The OA is B.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
We can create the equations:

25q + 5n = 470

5q + n = 94

and

n + q = 30

q = 30 - n

Substituting, we have:

5(30 - n) + n = 94

150 - 5n + n = 94

56 = 4n

14 = n

Answer: B

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