At a math convention, a poll is taken about cable news. It turns out that 7 out of every 12 people are bored by cable news. If there are 280 people at the convention who are bored by cable news, then how many people at the convention are not bored by cable news?

Guest May 16, 2023

#1**+1 **

Let \(x\) be the total number of people polled. We have the equation \(\frac{7}{12}x = 280\) which yields the solution \(x=480\) so there are \(480\) people in total. Since \(\frac{7}{12}\) of all people are bored by cable news, \(\frac{5}{12}\) are not, so the answer to the problem is \(\frac{5}{12} \cdot 480 = \boxed{200}.\)

lpieleanu May 16, 2023

#2**-1 **

*At a math convention, a poll is taken about cable news. It turns out that 7 out of every 12 people are bored by cable news. If there are 280 people at the convention who are bored by cable news, then how many people at the convention are not bored by cable news?*

Since 7 of 12 are bored, then it follows that 5 of 12 are not bored.

5

So ––– x 280 = 116**.**667

12

You can't have 2/3 of a person, so we call it **117 people who are not bored**

... or round it to 116 if that's the way your teacher wants to do it.

_{.}

Guest May 16, 2023