<PRE><B>Question 1150846</B>
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If algebra is not required, then you can solve this quickly with a bit of mental arithmetic.&lt;br&gt;
Since the sum and product are both whole numbers, the two numbers are almost certain to be whole numbers.&lt;br&gt;
You need their sum to be 12 and their product to be 35.&lt;br&gt;
There are many pairs of whole numbers whose sum is 12, but only one interesting one whose product is 35 -- 5 and 7.&lt;br&gt;
And the sum of 5 and 7 is 12, so you are done.&lt;br&gt;
If you are in a beginning algebra course, you want to know how to set up and solve the problem using formal mathematics. Here is one way....&lt;br&gt;
The sum of the two numbers is 12; then if x is one of the numbers, the other is (12-x).&lt;br&gt;
Now write and solve the equation that says the product of the two numbers is 35:&lt;br&gt;
{{{x(12-x) = 35}}}
{{{12x-x^2 = 35}}}
{{{0 = x^2-12x+35}}}&lt;br&gt;
To solve this by the usual algebraic method, you need to factor the quadratic expression into two linear factors.  To do that, you need to find two numbers whose sum is 12 and whose product is 35.&lt;br&gt;
But note that that is exactly what you needed to do to solve the problem without algebra....&lt;br&gt;
Nevertheless, you want to learn how to solve the problem using formal algebra; when the problems get more involved, you won&#39;t be able to solve them informally.  You will need to know how to solve them using algebra.&lt;br&gt;
{{{x^2-12x+35 = 0}}}
{{{(x-7)(x-5) = 0}}}&lt;br&gt;
{{{x = 7}}} or {{{x = 5}}}&lt;br&gt;
One of the numbers is x=7 and the other is (12-x) = 5; or one of the numbers is x=5 an the other is (12-x) = 7.  You get the same solution either way.&lt;br&gt;
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