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Akana has some dimes and some quarters. She has at most 25 coins worth a minimum of $4.45 combined. If Akana has 17 dimes, determine all possible values for the number of quarters that she could have. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.

 Sep 1, 2020
 #1
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This calls for "casework", though not much of counting...

 

We first need to figure out a "not so specific" range for quarters. We see that:

 

25 - 17 = 8

 

Which means, she can have from 1 to 8 quarters, but that is not specific enough. We also need to calculate the total amount of dimes she has:

 

0.1 * 17 = 1.7

 

Now, we can start:

 

If there were 1 quarter:

 

Not possible: not enough for the minimum amount of money

 

If there were 2 quarters:

 

Not possible: not enough for the minimum amount of money

 

If there were 3 quarters:

 

Not possible: not enough for the minimum amount of money

 

If there were 4 quarters:

 

Not possible: not enough for the minimum amount of money

 

If there were 5 quarters:

 

Not possible: not enough for the minimum amount of money

 

If there were 6 quarters:

 

Not possible: not enough for the minimum amount of money

 

If there were 7 quarters:

 

Not possible: not enough for the minimum amount of money

 

If there were 8 quarters:

 

Not possible: not enough for the minimum amount of money

 

so leave your answer blank.

 

BUT!

 

We could have saw from before whether there would have been enough money or not!

 

If we multiply: 8 * 0.25 = 2, and add that to 1.7, we get 3.7. Not possible.

 

What I don't understand about this problem is: If they literally said that Akana had some dimes and quarters, and they said that this was true, why did they give a possibility of "not possible"? Akana, you probably discovered Roman Numeral 0.

 

:)

 Sep 1, 2020

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