The sum of two numbers is 27 and the product is 182. The larger number is

To find the two numbers, we can set up a system of equations based on the information given in the problem.

Let's denote the two numbers as x and y.

From the problem, we know that:

1. x + y = 27 (the sum of the two numbers is 27)
2. xy = 182 (the product of the two numbers is 182)

We can solve this system of equations step by step:

Step 1: Solve the first equation for one variable. Let's solve for y:

y = 27 - x

Step 2: Substitute y in the second equation:

x(27 - x) = 182 27x - x^2 = 182 x^2 - 27x + 182 = 0

Step 3: Solve this quadratic equation. This can be factored into:

(x - 14)(x - 13) = 0

Setting each factor equal to zero gives the solutions x = 14 and x = 13.

Step 4: Substitute x = 14 and x = 13 into the equation y = 27 - x to find the corresponding values of y.

When x = 14, y = 27 - 14 = 13. When x = 13, y = 27 - 13 = 14.

So, the two numbers are 14 and 13.

The larger number is 14.