If one U. S. dollar is worth 0.690 English pounds, how many U. S dollars are needed to purchase an item that costs 350 dollars?

Something is wrong with your question, it must be 350 pounds.

So the approach for this question would be the use of unit analysis.

1 us dollar = 0.690 pounds

350 pounds * 1 dollar / 0.690 pounds = 507.24 dollars.

to check:507.24 dollars x 0.690 pounds / 1 dollars = 350 pounds