Question

There are 180 spectators at the football game. 79 of them are wearing a hat, 62 are wearing a scarf, and 27 are wearing a hat but not a scarf. How many spectators are wearing neither a hat nor a scarf?

Answer 1

By using set theory and subtracting those wearing hats, scarves, or both from the total, it is determined there are 91 spectators at the football game wearing neither a hat nor a scarf.

Step-by-step explanation:

To solve this problem, we need to use the concept of sets and find the number of spectators who are wearing neither a hat nor a scarf at the football game.

First, let's consider the total number of spectators, which is 180. Of these, 79 are wearing a hat and 62 are wearing a scarf. It is also given that 27 are wearing a hat but not a scarf. We need to find those wearing neither a hat nor a scarf.

Since 27 are wearing a hat and not a scarf, we can subtract them from the number who are wearing hats to find those wearing both a hat and a scarf, which is 79 - 27 = 52.

Now, we add the number of spectators wearing both to those wearing just a scarf to find the total number of scarf wearers: 52 + (62 - 52) = 62.

Adding the number of spectators wearing a hat, wearing a scarf, or both give us 79 + 62 - 52 = 89.

Therefore, the number of spectators wearing neither a hat nor a scarf is the total number of spectators minus those wearing a hat, a scarf, or both: 180 - 89 = 91.

So, 91 spectators are wearing neither a hat nor a scarf.