SOLUTION: What are all the possible combinations of coins( using pennies, nickels, dimes and quarters) that equal 43 cents.

Question 751645: What are all the possible combinations of coins( using pennies, nickels, dimes and quarters) that equal 43 cents.
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Here are all the possible ways to make 43 cents

3 pennies + 1 nickel + 1 dime + 1 quarter ... 6 coins total
8 pennies + 1 dime + 1 quarter ... 10 coins total
8 pennies + 2 nickels + 1 quarter ... 11 coins total
13 pennies + 1 nickel + 1 quarter ... 15 coins total
18 pennies + 1 quarter ... 19 coins total
18 pennies + 1 nickel + 2 dimes ... 21 coins total
18 pennies + 5 nickels ... 23 coins total
38 pennies + 1 nickel ... 39 coins total
43 pennies ... 43 coins total

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The only way to solve this is to find a logical way to list them.

Two quarters is 50 cents, so it is only possible to have either one quarter or zero quarters.

Start with 1 quarter. That leaves you with 18 cents to make up. So, given that you have 1 quarter, the most dimes you can have is 1, leaving you 8 cents to make up, so you can have, at most, 1 nickel, and then 3 pennies.

Now take away the nickel and add 5 pennies, so 1 Q, 1 D, 0 N, 8 P.

Take away the dime, so:

1 Q, 0 D, 3 N, 3 P, or
1 Q, 0 D, 2 N, 8 P, or
1 Q, 0 D, 1 N, 13 P, or
1 Q, 0 D, 0 N, 18 P

Take away the quarter, and now you can have up to 4 dimes:

0 Q, 4 D, 0 N, 3 P

And so on until you get down to 0 Q, 0 D, 0 N, 43 P. You can follow the pattern and then count the possibilities for yourself.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

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