SOLUTION: One number is 15 greater than the other number. The product of the two numbers is 286. Assuming both numbers are positive, find the numbers.

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Question 803861: One number is 15 greater than the other number. The product of the two numbers is 286. Assuming both numbers are positive, find the numbers.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let one number be x and the other number y
if one number is 15 greater than the other number, you have x=y%2B15....eq.1
if the product of the two numbers is 286, you have x%2Ay=286.....eq.2
solve the system:
x=y%2B15....eq.1....substitute in eq.2
x%2Ay=286.....eq.2
________________________
%28y%2B15%29%2Ay=286.....eq.2
y%5E2%2B15y=286
y%5E2%2B15y-286=0.......factor, write 15y as 26y-11y
y%5E2%2B26y-11y-286+=+0......group
%28y%5E2%2B26y%29-%2811y%2B286%29+=+0
y%28y%2B26%29-11%28y%2B26%29+=+0
%28y-11%29%28y%2B26%29+=+0
solutions:
if y-11++=+0 => y=11
if +y%2B26+=+0 => y=-26

Assuming both numbers are positive, we will use only highlight%28y=11%29 and calculate x
x=y%2B15....eq.1
x=11%2B15
highlight%28x=26%29
so, your numbers are highlight%28+26%29 and highlight%2811%29