Final answer:
To determine the expected number of sandwiches with pickles when 500 people were surveyed and 4 out of 9 like pickles, we use a proportion. Solving the proportion 4/9 = x/500 yields approximately 222, meaning about 222 sandwiches with pickles should be prepared.
Step-by-step explanation:
The student is asking how many sandwiches with pickles can be expected if 4 out of 9 surveyed people like pickles on their sandwich and 500 people were surveyed in total. To find this, we can set up a proportion where the ratio of people who like pickles (4 out of 9) is set equal to the unknown number of expected sandwiches with pickles (let's call this x) out of the total surveyed number (500).
The proportion is: 4/9 = x/500. To solve for x, we cross-multiply: (4)(500) = (9)(x). This gives us 2000 = 9x, and when we solve for x, we get x = 2000/9 ≈ 222.22. Hence, we can expect about 222 sandwiches with pickles.
However, since we cannot have a fraction of a sandwich, we round down to the nearest whole number, so the sandwich shop should expect to prepare 222 sandwiches with pickles.