One number is 10 less than twice a second number. Find a pair of such numbers so that their product is as small as possible.

I came up with 15 and 5 and those are incorrect

6 and 2?

incorrect

To find a pair of numbers such that their product is as small as possible, we can represent the numbers using variables and then set up an equation based on the given information.

Let's assume the first number is represented by 'x' and the second number is represented by 'y'.

According to the given information, "One number is 10 less than twice a second number." Mathematically, we can express this as:
x = 2y - 10

Now, we need to find a pair of values for x and y that minimizes their product, xy.

To do that, we can substitute the value of x from the equation above into the product expression:
xy = (2y - 10)y

Now, let's simplify the expression:
xy = 2y^2 - 10y

To find the minimum product, we can analyze the quadratic expression in terms of its graph or use calculus. In this case, let's use calculus to find the minimum.

We can differentiate the expression with respect to y and set it to zero to find the critical point where the minimum occurs:
d/dy (xy) = 2(2y) - 10 = 0
4y - 10 = 0
4y = 10
y = 10/4
y = 2.5

Next, substitute the value of y back into the equation x = 2y - 10:
x = 2(2.5) - 10
x = 5 - 10
x = -5

Therefore, the pair of numbers that minimizes their product is (-5, 2.5).