To find the answer to "What two numbers have a product of 45 and a sum of 70?" we first state what we know. We are looking for x and y and we know that x • y = 45 and x + y = 70.
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 = 70 and solve it for y to get y = 70 - x. Then, we replace y in x • y = 45 with 70 - x to get this:
x • (70 - x) = 45
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 45 and a sum of 70. The numbers are:
0.64887
69.35113
That's it! The two numbers that have a product of 45 and a sum of 70 are 0.64887 and 69.35113 as proven below:
0.64887 • 69.35113 ≈ 45
0.64887 + 69.35113 = 70
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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