Question

A blogger who is just starting out made three videos. So far, she has 312 subscribers, who watched one, two, or all three videos. The three videos got 740 total views all together. Assuming each subscriber only viewed a particular video once, how many more people watched all three videos than only one video?

Answer 1

116 more people

Explanation:

Let a, b, c signify the numbers of subscribers who watched 1, 2, and 3 videos, respectively. So we can say that:

a +b +c = 312 this means that there are 312 subscribers, total

a +2b +3c = 740 this means that there were 740 total views

Next, deduct the double the first equation from the second.

(a +2b +3c) -2(a +b +c)

= (740) -2(312)

this will give us: c -a = 740 -624 = 116

Therefore, 116 more people watched all three videos than watched one video.

hope this helps

Answer 2

116. Suppose x subscribers watched only one video, y watched two, and (312-x-y) watched three. There are 740 views in total, so x+2y+3(312-x-y)=740. -2x-y=-196, or 2x+y=196. The number of people who watched three videos is 312-x-y=312-(2x+y)+x=312-196+x=116+x. 116+x-x=116.