The product of two numbers is 120. The sum of the two numbers is 22. What are the two numbers?

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

From the problem, we have two equations:

1. x*y = 120 (The product of the two numbers is 120)
2. x + y = 22 (The sum of the two numbers is 22)

We can solve this system of equations step by step:

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

y = 22 - x

Step 2: Substitute y in the first equation:

x * (22 - x) = 120 22x - x^2 = 120 Rearrange the equation: x^2 - 22x + 120 = 0

Step 3: Solve the quadratic equation. This can be done by factoring, completing the square, or using the quadratic formula. The factored form of the equation is:

(x - 10)(x - 12) = 0

Step 4: Set each factor equal to zero and solve for x:

x - 10 = 0 or x - 12 = 0

So, x = 10 or x = 12

Step 5: Substitute x = 10 and x = 12 into the equation y = 22 - x to find the corresponding y values:

If x = 10, then y = 22 - 10 = 12 If x = 12, then y = 22 - 12 = 10

So, the two numbers are 10 and 12.