SOLUTION: The sum of two numbers is 33 and their product is 270. Find the two numbers.

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Question 1077493: The sum of two numbers is 33 and their product is 270. Find the two numbers.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let's the two numbers be x and y
if the sum of two numbers is 33, we have
x%2By=33 .............solve for x
x=33-y ....eq.1

and, if their product is 270, we have
x%2Ay=270 ...........solve for x
x=270%2Fy.......eq.2
since left sides of eq.1 and eq.2 are same, right sides are equal too
33-y=270%2Fy.......solve for y
%2833-y%29y=270
33y-y%5E2=270
0=y%5E2-33y%2B270...factor
0+=+y%5E2-15y+-18y+%2B270
0+=+%28y%5E2+-18y%29+-%2815y-270%29
0+=+y%28y+-18%29+-15%28y-18%29
0+=+%28y+-18%29%28y+-15%29
solutions:
if 0+=+%28y+-18%29=>y=18
if 0+=+%28y+-15%29=>y=15
now find x
x=33-y ....eq.1 if y=18
x=33-18
x=15
x=33-y ....eq.1 if y=15
x=33-15
x=18
so, your numbers are 15 and 18