To find the answer to "What two numbers have a product of 32 and a sum of 90?" we first state what we know. We are looking for x and y and we know that x • y = 32 and x + y = 90.
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 = 90 and solve it for y to get y = 90 - x. Then, we replace y in x • y = 32 with 90 - x to get this:
x • (90 - x) = 32
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 32 and a sum of 90. The numbers are:
0.35697
89.64303
That's it! The two numbers that have a product of 32 and a sum of 90 are 0.35697 and 89.64303 as proven below:
0.35697 • 89.64303 ≈ 32
0.35697 + 89.64303 = 90
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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