To find the answer to "What two numbers have a product of 105 and a sum of 44?" we first state what we know. We are looking for x and y and we know that x • y = 105 and x + y = 44.
Before we keep going, it is important to know that x • y is the same as y • x and x + y is the same as y + x. The two variables are interchangeable. Which means that when we create one equation to solve the problem, we will have two answers.
To solve the problem, we take x + y = 44 and solve it for y to get y = 44 - x. Then, we replace y in x • y = 105 with 44 - x to get this:
x • (44 - x) = 105
Like we said above, the x and y are interchangeable, therefore the x in the equation above could also be y. The bottom line is that when we solved the equation we got two answers which are the two numbers that have a product of 105 and a sum of 44. The numbers are:
2.53208
41.46792
That's it! The two numbers that have a product of 105 and a sum of 44 are 2.53208 and 41.46792 as proven below:
2.53208 • 41.46792 ≈ 105
2.53208 + 41.46792 = 44
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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