Travis Horner (Punkeroi@aol.com) proposed: .. > Each item costs more than one dollar and less than five dollars. .. > multiplied the cost of each item and arrived at the total $7.11 .. > then added the items together ... the total was still exactly $7.11. > (There was no sales tax involved) > What is the exact price of the item that cost the greatest amount?
Interesting - find the numbers given sum and product, but with decimals.
Usually, product problems call for factoring. Looking at the problem MOD some of the factors is also often helpful. But for both those we require whole numbers!
So here is your hint: Use cents instead of dollars. Prices: A/100, B/100, C/100, D/100 lead to ABCD/100000000=7.11 , and (A+B+C+D)/100 =7.11 (With 100<A,B,C,D<500.)
Clear the denominotors and you will have a problem about whole numbers. The factors are helpful. Looking at it MOD 5 (and remembering that all the numbers must between 100 and 500) really cuts down on the amount of work.
Robert |)|\/| || Burnaby South Secondary School |\| |firstname.lastname@example.org || Beautiful British Columbia Mathematics & Computer Science || (Canada)