SOLUTION: Ana has one coin of 5 cents, one coin of 10 cents, one coin of 20 cents and one coin of 50 cents. How many possible values she can make from these coins.

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Question 849807: Ana has one coin of 5 cents, one coin of 10 cents, one coin of 20 cents and one coin of 50 cents. How many possible values she can make from these coins.
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
No 1 2,3,4, or 5 of those coins add up to the same value
as any other 1,2,3,4, or 5, so every combination of coins
gives a different value.

There are two choices we can make for each coin.
They are:

1. Use it to form a value.
2. Do not use it to form a value.

There are 2 choices to make for the 5 cent coin. (Use it or don't).
There are 2 choices to make for the 10 cent coin.
There are 2 choices to make for the 20 cent coin.
There are 2 choices to make for the 50 cent coin.

Therefore there are 2×2×2×2 = 24 = 16 different values.
However that includes the value 0, in which case we do not use any 
coins.  So we exclude the value 0 from the 16:

Answer = 15 values (not counting 0 cents).

These values are every multiple of 5 cents from 5 cents through 85
cents, EXCEPT there is no way to have 40 cents or 45 cents.

Edwin

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