Question

number theory ?

"Ryan told Sam that he had 9 coins worth 45 cents. Sam said, 'There is more than one possibility. How many are pennies?' After Ryan answered truthfully, Sam said, 'Now I know what coins you have.' How many nickels did Ryan have?"

Why does it talk about pennies if no set amount is given? Is it implying I do something about pennies first?

The answer is 9 nickels, but the thing is... nobody said what types of coins he could possibly have, NOR did they say he has no pennies for sure.

Answer 1

If you have 5 pennies, that means that you need the remaining 4 coins to be worth 40 cents which can be easily be done with 4 dimes.

4 dimes + 5 pennies = 45 cents.

So when it says "After Ryan answered truthfully" I assume he said he has no pennies (otherwise there are multiple answers). So ... what if there are no pennies?

The smallest five coins you can use are then nickels.
5+5+5+5+5=25, so you need 20 cents with 4 coins. (Which is only 4 nickels)
Thus, 9 nickels overall.

If you start with a dime,
10=10, you will need 35 cents in 8 coins.
(I don't think it is possible without pennies, and even with pennies)

If you start with a quarter,
25=25, you will need 20 cents in 8 coins.
(no possible without nickels, and probably even with nickels not an option)

Answer 2

I see your logic, but I wonder why the answer acts like the question is concretely "he only has nickels"

Answer 3

So basically you can see that once we exclude nickels, we see that even 1 dime or even 1 quarter is not an option. Why? (Again)

If you start with a dime,
10=10, you will need 35 cents in 8 coins.
(I don't think it is possible without pennies, and even with pennies)

If you start with a quarter,
25=25, you will need 20 cents in 8 coins.
(no possible without nickels, and probably even with nickels not an option)

Answer 4

Thus, you can only use nickels.
And as you know 9\(\times\)5=45.

Answer 5

yes, the wording is pretty well off :)

Answer 6

I hope I am making sense(?)

Answer 7

basically ignore anything I posted about starting from five nickels.
You just know (as I posted) that dimes and quarters are excluded.

Answer 8

I see what you mean, thank you :-)

Answer 9

Thank you = Thank you.
Can't be factored.

sad[voindwv
sdadpvc --> ekks
aascodvdv + jdsnms ** jdnmd &.

Answer 10

good luck :))

Answer 11

LOL. Also thank you for that haha