Solving a simple addition / multiplication puzzle.

[matalog]

My dad forwarded me an email I had sent him in 2002:

"A customer at a 7-11 store selected four items to buy, and was told that the cost was $7.11. He was curious that the cost was the same as the store name, so he inquired as to how the figure was derived. The clerk said that he had simply multiplied the prices of the four individual items. The customer protested that the four prices should have been ADDED, not MULTIPLIED. The clerk said that that was OK with him, but, the restult was still the same: exactly $7.11. What were the four prices?"

So, obviously we have a+b+c+d =7.11= a*b*c*d.

I must have took the time to work it out on paper back then, but now I have my HP Prime.

To be honest, I usually use this calculator to do something different regarding connectivity or fast processing on a mobile computer, but I rarely use it for these type of real world problems and need some help.

Is there a way to input those 2 equations, and get a solve app or command on the HP Prime to return the answers?

I suppose that the answers will be 2dp each, and not more.

I tried this in CAS

Code:

solve( { a+b+c+d=7.11, a+b+c+d=7.11}, {a, b, c, d})

but it resulted in a far more complicated answer than I assume the writer of the puzzle had in mind :-).