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# word problem

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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
+1042
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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

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