Problem Solving

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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He has 6 coins, and he has two types of coins, including nickels. If he has only nickels and dimes, he could have at most 60 cents. But he has 70 cents, so he must have nickels and quarters.

Since he must have at least 1 quarter, and can't have 3 or more (then he'd have more than 70 cents), there are only two simple possibilities to check: he can have 1 quarter or 2 quarters. Testing each, we find he has 2 quarters and 4 nickels.

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

The only way one can make 70 cents using 6 coins in two types of coins is 2 quarters and 4 nickels. Therefore, Pat is holding 4 nickels.

Answer: C