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?
We can start the problem by using the ratio of people who are bored by cable news to the total number of people at the convention. The ratio is 7/12, which means that for every 12 people at the convention, 7 of them are bored by cable news.
To find out the total number of people at the convention who are bored by cable news, we can set up a proportion:
7/12 = 280/x
where x is the total number of people at the convention.
To solve for x, we can cross-multiply:
7x = 12 * 280
7x = 3360
x = 480
So there are 480 people at the convention in total. To find out how many of them are not bored by cable news, we can subtract the number of people who are bored from the total:
480 - 280 = 200
Therefore, there are 200 people at the convention who are not bored by cable news.
To find out how many people at the convention are not bored by cable news, we need to subtract the number of people who are bored by cable news from the total number of people at the convention.
Given that 7 out of every 12 people are bored by cable news, we can set up the following proportion:
7/12 = 280/x
To solve for x, we can cross-multiply:
7x = 280 * 12
7x = 3360
Next, divide both sides of the equation by 7 to isolate x:
x = 3360/7
x = 480
Therefore, there are 480 people at the convention who are not bored by cable news.