TV ratings question wherein the variable is tied to a percentage and the answer isn't through simple addition.

Question

TV ratings- A broadcast gets a 4.6 rating from markets comprising 65% of the population. The broadcast's final rating when 100% of the markets report in is 3.2. What rating did the broadcast get in the markets covering the other 35% of the population to result in a final rating of 3.2?

Answer 1

This is a weighted average problem.

Let x be the rating the broadcast get in the markets covering the other 35% of the population, then

0.65 (4.6) + 0.35x = 3.2

 

Solve this equation for x to get the answer you need. (x = 0.6)