# If x and y are positive integers with x+y

If x and y are positive integers with x+y

what is the possible largest product of x and y?
mindy129
15 August 2012
so mistake there. i'll retype the full question. If x and y are positive integers with x+y
mindy129
15 August 2012
Unfortunately you still haven't typed out the full question - you might need to try one more time?
jim360
16 August 2012
OK having said that, assuming the problem is along the lines of: "If x and y are two positive integers with x+y = 20, what is the largest possible product of x and y?" Then there are two reasonable ways to approach this problem. The first is by trial and error. Suppose x+y = 20, then all the possible pairs of x and y are (1,19) (2, 18), (3, 17), etc., all the way up to (10,10). You'll see that in each pair the total is 20, of course, so these are possible values for x and y. Now, just take the product xy for each pair! You'll get 119=19, 218=36, etc., and then find which pairing gives the largest answer, and that's your full answer. Of course, this method shouldn't be relied on, if the sum x+y were large. However it does lead you to the right answer, and may suggest the general answer if you look closely at the final result you get in this case and how it relates to the starting information. More later - since I may have misunderstood the problem I don't want to go into details yet.
jim360
16 August 2012
if x and y are positive integers with x+y
mindy129
17 August 2012
A handy tip I've found to using this site is that you should prepare your messages in Notepad or word or similar and then paste them in here. Saves the trouble of hitting enter too soon.
jim360
17 August 2012
well yes because of copy and paste this is what happen and i don't press enter all by accident.
mindy129
24 August 2012
Building on Jim360's good start -
malvernmaths
25 August 2012
You will notice that a pattern occurs. What happens to the product as it gets to the end of the sequence? 1x19 = 19 2x18 = 36 3x17 = 51 . . . 17x3 = 51 18x2 = 36 19x1 = 51 Notice that we get an increasing product, then it decreases in the same pattern at the end. So somewhere in the middle of the sequence we will get a product that 'tops out' before decreasing again. So, what are the 2 numbers in the middle of the sequence? (Remember that they can be equal)
malvernmaths
25 August 2012