a teacher surveys her class of 27 students to learn how many enjoy playing the video game mario kart 7 (mk7) and its newer version mario kart 8 (mk8). she finds that 7 students play only version 7 and that 5 play only the newer version. if twice as many students play both versions as those that play neither version, how many students play mario kart 7?

17

Step-by-step explanation:

We set up a Venn diagram with two circles using the provided info:

Now, we know 7+2x+5+x=27, so x=5. Since the problem asks for Mario Kart 7 (MK7) players, this is 7+2x=17.

Number of students playing mario kart 7 = 17

Step-by-step explanation:

Total number of students in class = 27

Number of students playing only version 7 = 7

Number of students playing only version 8 = 5

Remaining number of students = 27 - 7 - 5 = 15

This includes students play both versions and students that play neither version

So total number of students play both versions and students that play neither version = 15

Given that twice as many students play both versions as those that play neither version.

Let x be the number of students that play neither version.

So number of students playing both versions = 2x

We have

x + 2x = 15

3x = 15

x = 5

Number of students playing both versions = 2x = 10

Number of students playing mario kart 7 = 7 + 10 = 17

Number of students playing mario kart 7 = 17