BTGmoderatorDC wrote:Pat has a pocket full of quarters, dimes, and nickels. He takes 6 coins out of his pocket that amount to $0.70. If there are only two denominations of coins among the 6 coins in Pat's hand, how many nickels is he holding? (quarter = 25 cents, dime = 10 cents, nickel = 5 cents)
A. 2
B. 3
C. 4
D. 5
E. 6
OA C
Source: Princeton Review
Say
the number of quarters, dimes, and nickels Pat has are x, y and z, respectively. It is known that x, y and z are positive integers.
Since the question ask for the number of nickles, Pat must have either quarters, and nickels or dimes, and nickels
Case 1: Say Pat has 6 coins that are quarters and nickels
Thus, 25x + 5z = 70 and x + z = 6. Upon solving, we get z = 4. This is the answer.
There is no need to deal with Case 2. However, for the sake of understanding, we do so.
Case 2: Say Pat has 6 coins that are dimes and nickels
Thus, 10y + 5z = 70 and y + z = 6. Upon solving, we get z = -2 (not a positive value). This cannot be the answer.
The correct answer:
C
Hope this helps!
-Jay
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