$7.11 word problem

I need to verify that my answer(logic) is correct. I got this word problem from a magazine recently:
A person goes into a store and buys 4 items totaling $7.11.
The price of the 4 items will equal $7.11 if added(of course) but also if multiplied.
What is the price of each item?

Kid Funky Fried

This is an old classic.

So, what are your answers?. There are only 4 that work perfectly.

You should be able to check on a calculator.

Well here is what i did-
It seemed that I was unable to use alegbra because i could not eliminate enough varibles to solve for any given one. So, because the numbers were to be multiplied, I found all the factors of 711-1,3,9,79,237,and 711.Of these factors I found 3 & 2.37 would be the two numbers that I felt meant the conditions. Having then found all the factors of those numbers I concluded, now it seems in error, that there are no possible solutions.

Kid

Try these:

$1.20, $1.25, $1.50, $3.16

Thanks, can you show me how you got the answers?

Trial and error. Years ago. This is an old problem.

Actually, if I remember correctly, I started with 1.2 ,1.25, 1.5.

These three were just a lucky start and I knew they also have the same sum and product.

Then it was a matter of finding one more number which made 7.11

Had I factored 7110 and not 711 I would have found the numbers I was looking for.

Thanks for your help!

those are prime factors correct?