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.

Guest Sep 1, 2020

#1**+2 **

**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.**

**:)**

ilorty Sep 1, 2020