Question 988350: joey dumped the change out of his pocket and found that he had 25 coins totaling exactly $1.00 what coins might joey have had in his pocket? Plz help
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
First thing to note is that you must have some pennies. That is because if you had all nickels, you would only have 20 coins.
Second, you must have a number of pennies that is divisible by 5, because if you have some number of pennies NOT divisible by 5, you can't get to an even dollar no matter how many coins you have.
Third, you can't have as many as 25 pennies, because that would account for all 25 coins, but you only have 25 cents.
So, let's examine the situation if you have 20 pennies. That means that you would have to make 80 cents from 5 coins consisting of quarters, dimes, and nickels.
Is it possible to do this if you have zero quarters? No, because the most you can have with five coins if none of them are quarters is 50 cents, but we need 80 cents.
Is it possible to do this if you have one quarter? No, because 80 minus 25 is 55, and the most you can have is 40 if the remaining four coins are dimes.
Is it possible to do this if you have three quarters? No, because 80 minus 75 is 5, and there is no way to make 5 cents with two coins.
So far we have proven that if 20 of the coins are pennies, then two of the other coins must be quarters. I sense we are tantalizingly close to a solution here.
I'll let you finish. Let me know what you come up with.
By the way, there are also solutions that have 15 or 10 pennies.
John
My calculator said it, I believe it, that settles it
|
|
|
