Let $n$ be the smallest composite number such that it can be written as the product of two positive integers that differ by 10?

The smallest composite number for is 24, which is the product 2 and 12.

Step-by-step explanation:

A composite number is an integer that is not a prime number, that is, a number that can be divided only by one and itself. Let be the smallest composite number such that there are two positive integers , such that and . is a positive integer, since both integers are positive. Then, we can use the following formula:

(1)

We obtain the roots of this second order polynomial by means of the Quadratic Formula:

(2)

Given that , we must observe the following inequation:

(3)

Let is find the values of x and y by iterative means:

x = 11, y = 1

11 is not a composite number, but a prime number.

x = 12, y = 2

24 is a composite number, which contains the following product of prime numbers:

The smallest composite number for is 24, which is the product 2 and 12.

(2,20) means that the 2 is 2 hours and 20 is 20$. so there both 20$ for 2 hours only the same price. like it says. so, the dunk tank and the bounce house are the same price (20$) for the same amount of time (2 hours).

hope i