SOLUTION: Natalie and Courtney each have 49 cents and they each have 12 coins. Natalie has a coin with a value different from any of Courtney's. How many nickels does Courtney have?

Question 81627: Natalie and Courtney each have 49 cents and they each have 12 coins. Natalie has a coin with a value different from any of Courtney's. How many nickels does Courtney have?
Answer by mathdoc314(58) (Show Source): You can put this solution on YOUR website!

ok this is a pretty fun word problem.
I think there is no 2c piece in this problem so I guess coins here are going to be 1c, 5c, 10c, 25c
It looks to me like the number of pennies has to be 9 or 4 because all the other coins are divisible by 5 and 49 divided by 5 has remainder 4 and you only get 12 coins so you can not have 14 pennies or 19 or 24 or 29 etc.
So suppose there are 9 pennies and then you get 3 coins to make 40 cents which could be 1 quarter, 1 dime, and 1 nickel So that is one way
9 pennies 1 nickel 1 dime 1 quarter.
The problem talks about Natalie having a coin that Courtney does not have. The solution 9 pennies 1 nickel 1 dime 1 quarter has all four kinds of coin which is every kind of coin so that can not be Courtney and that would have to be Natalie because there are only two girls.
Then what if there are 4 pennies? You would have 8 coins to make 45 cents. If you try having a quarter then you would have 7 coins to make 20 cents out of dimes and nickels which I don't think is possible. So you have 8 dimes and nickels to make 45 cents which I think has to be 1 dime and 7 nickels. This is the only other solution I can think of.
So my answer is Courtney has 4 pennies, 7 nickels, and 1 dime
and Natalie has 9 pennies, 1 nickel, 1 dime, and 1 quarter.
These puzzles are more fun if you think them thru yourself instead of posting them to an internet site and letting someone else type the answer to you! Also with an internet site you can get the wrong answer! or you may have to wait and wait! It is not always the best way!
Hope this answer helps

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