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?

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

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.