In a "seven-eleven" (7-11) store, a customer selected four items to buy. The check-out clerk says that he multiplied the costs of the items and obtained exactly 7.11, the very name of the store! The customer calmly tells the clerk that the costs of the items should be added, not multiplied. The clerk then informs the customer that the correct total is also $7.11.
What are the exact costs of the 4 items?
any help will be much appreciated
I think that you'll need some intelligent trial and error here, starting with the factors of 711.
The prime factors of 711 are 3 x 3 x 79.
We can use this to find four numbers with no more than 2 decimal places that multiply together to make 7.11. For instance:
1.00 x 3.00 x 3.00 x 0.79 = 7.11
Now these numbers have got to add up to 7.11 as well. So let's check these numbers: 1.00 + 3.00 + 3.00 + 0.79 = 7.79. Not bad as a starting guess, but not quite right. We need to make the sum of the four numbers a bit smaller, without altering their product.
Try halving one of the three's (that will take away 1.50 from the total) and doubling the 0.79 (which will put 0.79 back) - this will make the total smaller:
1.00 x 3.00 x 1.50 x 1.58 = 7.11
1.00 + 3.00 + 1.50 + 1.58 = 7.08 - so close!
It's a bit hard not to go straight to the answer now - because someone has already told you what it is. But you can try to imagine you don't know the answer, and try again (and again...) until you come up with the right total. As long as you divide one of the four numbers by something and multiply another number by the same thing, the product will stay the same.
I guessed at dividing one of the 3.00's by 2, to give 1.50. But you could divide 3.00 by 3, 4, 5, 6, 10, 15, ... anything that gives a whole number of pence (or cents, depending on your currency).
I don't think there's any other way of doing it. Unless, of course, someone out there knows different...