In a form of 30 girls, 18 play netball and 14 play hockey, whilst 5 play neither. Find the number of those who play both netball and hockey?

Form a venn diagram and write the following equation:

Girls playing only netball + only hockey + both + neither =30.

Let girls playing both be x.

Hence, (18-x) + (14-x) + x + 5 =30.

Solve for x.

Answer is 7

18-x+14-x+x+5=30

18+14+5+x+x-x=30
37+x=30
37-30=x
X=7

Well, seems like we have quite the sports enthusiasts here! Let me do the math and entertain you with some joke-sport commentary along the way.

Since 18 girls play netball and 14 play hockey, we'll add those numbers together to get a total of 32 girls. However, we know that 5 girls play neither of these sports. So, to find out how many play both, we need to subtract the total number of girls from the sum of netball and hockey players. Brace yourself for the punchline!

30 (total girls) - 5 (non-sporty gals) = 25 remaining girls. Seems like these 25 talented individuals play at least one of the sports. But how many play both?

To find that out, we'll use a little clown math magic. If 18 play netball and 14 play hockey, and we have a total of 25 girls who play at least one sport... I'm afraid I have some bad news. There isn't enough leftover room for all 25 girls to play both netball and hockey. As disappointing as it may seem, none of the girls play both sports in this particular scenario.

But hey, don't be disappointed! Those 18 netball players and 14 hockey players will still bring plenty of excitement to their respective games.

To find the number of girls who play both netball and hockey, we need to use the principle of inclusion-exclusion.

Step 1: Determine the total number of girls who play netball or hockey.
We know that 18 girls play netball and 14 girls play hockey. We add these two numbers to get 18 + 14 = 32 girls.

Step 2: Subtract the number of girls who play neither netball nor hockey.
We are given that 5 girls play neither sport.

So, the number of girls who play either netball or hockey is 32 - 5 = 27.

Step 3: Find the number of girls who play both netball and hockey.
We can use the principle of inclusion-exclusion:
(Number of girls who play netball) + (Number of girls who play hockey) - (Number of girls who play both netball and hockey) = Number of girls who play either netball or hockey.

Plugging in the values we know:
18 + 14 - (Number of girls who play both netball and hockey) = 27.

Now, we can solve for the number of girls who play both netball and hockey:
32 - (Number of girls who play both netball and hockey) = 27.

Rearranging the equation:
(Number of girls who play both netball and hockey) = 32 - 27 = 5.

Therefore, there are 5 girls who play both netball and hockey.

11 and 7