SOLUTION: Find the numbers whose sum is 27 and product is 182.
Ans:let the numbers are x and (27-x).ect..............
In this case why we are taking (27-x)
I'll answer your second question first:
If we know that
then, isn't it obvious that
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The first number = x
The second number = 27-x
x-13 = 0; x-14 = 0
x = 13; x = 14
If
The first number = 13, then
the second number = 27-13 = 14
Or if
The first number = 14, then
the second number = 27-14 = 13
You can take your pick as to which you call
"the first number" and which you call
"the second number".
Either way they are 13 and 14.
Edwin
You are calling the second number 27-x, because the sum of x and (27-x) is 27 -- as the problem requires.
So the two numbers are x and (27-x), and their product is 182:
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.
But that's exactly what the original problem asked you to do. So the formal algebra doesn't help to solve the problem.
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.
182 = 2*91 = 2*7*13
It should be easy to see that you want to combine the first two factors to get
182 = 14*13
14+13 = 27, so 14 and 13 are the numbers you are looking for.
