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

Cheers,
Brent

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

GMAT assassins aren't born, they're made,
Rich