Question

In a group of Explore students, 38 enjoy video games, 12 enjoy going to the movies and 24 enjoy solving mathematical problems. Of these, 8 students like all three activities, while 30 like only one of them.
How many students like only two of the three activities?

Answer 1

Answer:

Step-by-step explanation:

We can see that

the one group of letters add up to 21 (26–5 = 21)

the next group of letters add up to 27 (32–5 = 27)

the last group of letters add up to 25 (30–5 = 25)

Your question tells us that A+B+C = 37

We count each of the values (A+B+C) once each

We count each of the values (x+y+z) twice each

We count the middle number (5) three times

We know that the sum of all these numbers is equal to the sum of the red numbers.

26 + 32 + 30 = 88

Put together everything that we know:

(A+B+C) + 2 × (x + y + z) + 3 × (5) = 88

(37) + 2 × (x + y + z) + (15) = 88

52 + 2 × (x + y + z) = 88

I bet you can finish the work from here.

subtract 52 from both sides

divide both sides by 2

what did you get