Question Video: Finding the Arithmetic Mean between Two Numbers in Terms of 𝑥 Mathematics

Video Transcript

Find in terms of 𝑥, the arithmetic mean of eight 𝑥 plus eight and six 𝑥 plus 22.

To find an arithmetic mean, we divide the sum of the values by the number of values. In this instance, we have two values: eight 𝑥 plus eight and six 𝑥 plus 22. We need to take the sum of these two values and divide by two. We can simplify the numerator by combining like terms. Eight 𝑥 plus six 𝑥 equals 14𝑥, and eight plus 22 equals 30. We can rewrite our numerator as 14𝑥 plus 30 and then divide this numerator by two. As both terms in the numerator are even, we simply divide 14𝑥 by two and divide 30 by two. 14𝑥 divided by two is seven 𝑥, and 30 divided by two is 15.

The arithmetic mean of eight 𝑥 plus eight and six 𝑥 plus 22 is equal to seven 𝑥 plus 15. It’s also worth noticing that seven 𝑥 is halfway between six 𝑥 and eight 𝑥, and 15 is halfway between eight and 22. This means that it would’ve been possible to work out the arithmetic mean in this case by inspection. In either case, you would find that the arithmetic mean is seven 𝑥 plus 15.