Question

A chain restaurant has hundreds of locations in the United States. The three states with the most locations are Alabama, South Carolina, and Florida. Let the set U be all the locations of the restaurant in the United States and let the sets A, S, and F be the locations in Alabama, South Carolina, and Florida, respectively.

The following Venn diagram depicts the three states with the most locations and the cardinal number for each set is shown. How many of the restaurants are in the United States but not in the three states in the diagram?

Answer 1

There are 253 locations of the restaurant in the United States that are not in Alabama, South Carolina, or Florida.

The Venn diagram provided shows the number of locations for a chain restaurant in three specific states and the total number of locations in the United States. To find the number of restaurants in the United States but not in the three states (Alabama, South Carolina, and Florida), we need to subtract the number of locations in these states from the total number of locations in the United States.

Given:

- Total number of locations in the United States: U = 546

- Number of locations in Alabama: A = 46

- Number of locations in South Carolina: S = 104

- Number of locations in Florida: F = 143

Assuming there are no overlaps between the locations in Alabama, South Carolina, and Florida (as the Venn diagram does not show any intersections), the calculation would be:

U - (A + S + F)

Plugging in the values:

546 - (46 + 104 + 143)

Now, calculate the result to find the number of restaurants in the United States but not in the three states.

Number of locations not in Alabama, South Carolina, or Florida:

253

Therefore there are 253 locations of the restaurant in the United States that are not in Alabama, South Carolina, or Florida.