# The difference between two numbers is 10 and their product is 3000. What are the two numbers?

The difference between two numbers is 10 and their product is 3000. The difference between two numbers is 10

Which would mean x - y = 10, because x and y are two different numbers and "difference" is a keyword for subtracting.
Their product is 3000

Which would mean x * y = 3000, because "product" is a keyword for "multiplying".

Now we have two equations we can use to obtain the values of x and y, which are: X - y = 10 and x * y = 3000.

Let's take the first equation and solve for x, and then solve for y.

x - y = 10

x = 10 + y

y = x - 10

Now let's plug these in into the multiplication equation. But we need to only plug one variable at a time. Observe:

x * y = 3000

x * (x - 10) = 3000

x^2 - 10x = 3000

x^2 - 10x - 3000 = 0

To solve for x here, we need to use the quadratic formula, which is $x=frac{-bpmsqrt{b^2-4ac }}{2a}.$ B represents the constant in front of the "x", A stands for the constant in front of the "x^2", and C stands for just the constant without any variable (which would be the -3000).

x = {10 ± √(-10)^2 - 4(1)(-3000)}/2(1)

x = (10 ± √100 + 12000)/2

x = (10 ± √12100)/2

x = (10 ± 110)/2

We have two values for x:

x = (10 + 110)/2 = 120/2 = 60

x = (10 - 110)/2 = -100/2 = -50

Now that we know what x could be, let's plug them back into the original equations.

x = 10 + y

60 = 10 + y

50 = y (Therefore, if x is 60, y must be 50. And it works. Plug these numbers into the equations and they will be equal.)

However, we had a second number for x. Let's plug that in.

x = 10 + y

-50 = 10 + y

-60 = y (If x = -50, then y must be -60. These also work for the original equations when you plug them in, mainly because multiplying two negatives together cancel out the negative signs.)

So you can have: x = 60 and y = 50 OR x = -50 and y = -60.

thanked the writer.