Question 1162006
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You are calling the second number 27-x, because the sum of x and (27-x) is 27 -- as the problem requires.<br>
So the two numbers are x and (27-x), and their product is 182:
{{{x(27-x) = 182}}}
{{{27x-x^2 = 182}}}
{{{x^2-27x+182) = 0}}}<br>
To solve this using algebra, you need to factor the quadratic expression by finding two numbers whose sum is 27 and whose product is 182.<br>
But that's exactly what the original problem asked you to do.  So the formal algebra doesn't help to solve the problem.<br>
To find the answer, find the prime factorization of the product 182 and use it to find a way to write 182 as the product of two numbers whose sum is 27.<br>
182 = 2*91 = 2*7*13<br>
It should be easy to see that you want to combine the first two factors to get<br>
182 = 14*13<br>
14+13 = 27, so 14 and 13 are the numbers you are looking for.<br>
ANSWER: 14 and 13<br>