SOLUTION: The toll for a car crossing a certain bridge is 50c. The machines in the 'exact change' lanes accept any combination of coins that total exactly 50c, but they do not accept 1c or 5

Question 1154332: The toll for a car crossing a certain bridge is 50c. The machines in the 'exact change' lanes accept any combination of coins that total exactly 50c, but they do not accept 1c or 50c coins. In how many different ways can a driver pay the toll in the 'exact change' lane?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

I will assume this problem is using American coins, which means the denominations that can be used are 25c, 10c, and 5c.

In that case, the number of different combinations of coins that can make the required 50c is easy to determine quickly, using an organized list.

For each possible number of quarters (there are only three -- 0, 1, or 2), you only need to determine the possible numbers of dimes you can use, because whatever remains after the quarters and dimes can be made using nickels.

(a) 2 quarters.
That makes the whole 50 cents; there is only one choice for the number of dimes: 0.
So 1 way to make 50 cents using 2 quarters.
(b) 1 quarter.
That makes 25 cents, there is 25 cents remaining. The number of dimes can be 0, 1, or 2.
So 3 ways to make 50 cents using 1 quarter.
(c) 0 quarters.
The whole 50 cents still remains; the number of dimes can be 0, 1, 2, 3, 4, or 5 -- 6 choices.
So 6 ways to make 50 cents using 0 quarters.

ANSWER: 1+3+6=10 ways to pay the 50c toll using quarters, dimes, and nickels.

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