SOLUTION: The sum of two numbers is 12. Three times the product of the number is 105. What are the numbers?

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Question 27769: The sum of two numbers is 12. Three times the product of the number is 105. What are the numbers?

Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two numbers be a and b.
You can write two equations from the problem description.
a+%2B+b+=+12 Solve this one for a and substitute into the second equation. a+=+12-b
3ab+=+105
3%2812-b%29b+=+105 Simplify and solve for b.
36b+-+3b%5E2+=+105 Subtract 105 from both sides of the equation.
36b+-+3b%5E2+-+105+=+0 Multiply through by -1.
3b%5E2+-+36b+%2B+105+=+0 Factor out a 3.
3%28b%5E2+-+12b+%2B+35%29+=+0 Apply the zero products principle.
b%5E2+-+12b+%2B+35+=+0 Factor this quadratic equation.
%28b+-+7%29%28b+-+5%29+=+0 Apply the zero products principle again.
b+-+7+=+0 and/or b+-+5+=+0
If b+-+7+=+0 then b+=+7
If b+-+5+=+0 then b+=+5
The two numbers are: 5 and 7