SOLUTION: How do I explain the answer to this question? I am thinking of two numbers. When they are multiplied, the product is 36, when they are added, the sum is 15, what are the two numbe

Algebra ->  Equations -> SOLUTION: How do I explain the answer to this question? I am thinking of two numbers. When they are multiplied, the product is 36, when they are added, the sum is 15, what are the two numbe      Log On


   

Question 242608: How do I explain the answer to this question?
I am thinking of two numbers. When they are multiplied, the product is 36, when they are added, the sum is 15, what are the two numbers?
I am suppose to create a equation (x+ 2 - 5.00 = 2.00, something like that)
I know the answer is 12 and 3 but how do I put it into an equation?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two numbers be represented by x and y
You are told " When they are multiplied, the product is 36, when they are added, the sum is 15, what are the two numbers?"
So
x+%2A+y+=+36

x+%2B+y+=+15 isolate x
x+=+15-y use this value for x in the first equation

x+%2A+y+=+36
%2815-y%29%2Ay+=+36 expand
15y+-+y%5E2+=+36 collect into quadratic form
0+=+y%5E2+-15y+%2B36 factor
0+=+%28y-3%29%28y-12%29 For a product to be zero,one or more factors must be 0
So
y-3=0 or y-12=0
y = 3 or y = 12
The two numbers are 3 and 12