Question

two consecutive even positive integers have a product of 2,400. what is the smaller of the two numbers?

Answer 1

48 * 50 = 2400

so the smaller will be 48

hope this will help you

Answer 2

Answer: The smaller of the two numbers is 48.

Step-by-step explanation: Given that the product of two consecutive even positive integers is 2400.

We are to find the smallest of the two numbers.

Let n and (n + 2) be the given consecutive even positive integers.

Then, according to the given information, we have

`n*(n+2)=2400\\\\\Rightarrow n^2+n=2400\\\\\Rightarrow n^2+n-2400=0\\\\\Rightarrow n^2+50n-48n-2400=0\\\\\Rightarrow n(n+50)-48(n+50)=0\\\\\Rightarrow (n-48)(n+50)=0\\\\\Rightarrow n-48=0,~~~~~n+50=0\\\\\Rightarrow n=48,~-50.`

Since we are considering positive integers, so n = 48.

Therefore, the other even positive integer will be

`n+2=48+2=50.`

That is, the two consecutive even positive integers are 48 and 50.

Thus, the smaller of the two numbers is 48.