The sum of two numbers is 27 and product is 182 . Thenumbers are: 10 and 15 18 and 14 12 and 15 11 and 24

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Denote numbers x and y: Let's denote the two numbers as x and y. According to the problem, we have two equations: 1) x + y = 27 (Sum of the two numbers) 2) xy = 182 (Product of the two numbers) We need to find the values of x and y that satisfy both equations.Express y in terms of x: We can express y in terms of x using the first equation: y = 27 - x.Substitute y into second equation: Now we substitute y = 27 - x into the second equation to find x: x(27 - x) = 182 Expanding this, we get: 27x - x^2 = 182Rearrange to form quadratic equation: Rearrange the equation to form a quadratic equation: x^2 - 27x + 182 = 0Factor quadratic equation: We can factor this quadratic equation to find the values of x: (x - 14)(x - 13) = 0Find possible values for x: Setting each factor equal to zero gives us the possible values for x: x - 14 = 0 or x - 13 = 0 So, x = 14 or x = 13Calculate corresponding values for y: If x = 14, then y = 27 - x = 27 - 14 = 13. If x = 13, then y = 27 - x = 27 - 13 = 14.Check product for both pairs: We check the product for both pairs to ensure there's no math error: For x = 14 and y = 13: 14 * 13 = 182 For x = 13 and y = 14: 13 * 14 = 182 Both pairs give the correct product, so there is no math error.

The sum of two numbers is $27$ and product is $182$ . The numbers are: $\newline$ $10$ and $15$ $\newline$ $18$ and $14$ $\newline$ $12$ and $15$ $\newline$ $11$ and $24$

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The sum of two numbers is $27$ and product is $182$ . The numbers are: $\newline$ $10$ and $15$ $\newline$ $18$ and $14$ $\newline$ $12$ and $15$ $\newline$ $11$ and $24$