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To determine the total number of sandwiches sold at lunchtime, we start by understanding the relationship given in the problem:

1. Percentage Representation: We know that 14 percent (or 0.14 as a decimal) of the total sandwiches sold are turkey sandwiches.

2. Quantity Information: We are given that 28 turkey sandwiches were sold.

Now, let's use these details to find out the total number of sandwiches sold:

1. Set up the equation:
The percentage of turkey sandwiches (14%) times the total number of sandwiches (let's denote this total number by \(\( T \)\)) gives us the number of turkey sandwiches sold. This relationship can be set up as:
\(\[ 0.14 \times T = 28 \]\)

2. Solve for \(\( T \)\):
To isolate \(\( T \)\), we need to divide both sides of the equation by 0.14:
\(\[ T = \frac{28}{0.14} \]\)

3. Calculate the total number of sandwiches:
Performing the division:
\(\[ T = 200 \]\)

Therefore, the total number of sandwiches sold at lunchtime is 200.

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