Q: What two numbers have a product of 27 and a quotient of 3?

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This problem cannot be completed with real numbers because the highest possible product of two numbers that add up to 27, which is 13.5*13.5=182.25, is nowhere even close to 504.

189

27/2025 = 1/75 = 0.0133...

The numbers are 26 and 27.

Let the first number be x and the second number is 27 − x. [As the sum of both the numbers is 27] Therefore, their product = x (27 − x) It is given that the product of these numbers is 182. x (27 – x) = 182 x2 + 27x - 182 = 0 Changing the signs on both sides we get,x2 - 27x + 182 = 0 Factorizing we get , 13 and 14 are the numbers whose sum is 27 and product is 182 x2 – 13x – 14x + 182 = 0 = x(x – 13) – 14 (x – 13)= 0 = (x – 13) (x – 14) = 0 Either x – 13 = 0 or x − 14 = 0 i.e., x = 13 or x = 14 If first number = 13, then Other number = 27 − 13 = 14 If first number = 14, then Other number = 27 − 14 = 13 Therefore, the numbers are 13 and 14.

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