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Algebra / Linear equations in two variables Difficulty: Easy

An employee at a restaurant prepares sandwiches and salads. It takes the employee $1.5$ minutes to prepare a sandwich and $1.9$ minutes to prepare a salad. The employee spends a total of $46.1$ minutes preparing $x$ sandwiches and $y$ salads. Which equation represents this situation?

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Explanation

Choice B is correct. It’s given that the employee takes $1.5$ minutes to prepare a sandwich. Multiplying $1.5$ by the number of sandwiches, $x$ , yields $1.5 x$ , the amount of time the employee spends preparing $x$ sandwiches. It’s also given that the employee takes $1.9$ minutes to prepare a salad. Multiplying $1.9$ by the number of salads, $y$ , yields $1.9 y$ , the amount of time the employee spends preparing $y$ salads. It follows that the total amount of time, in minutes, the employee spends preparing $x$ sandwiches and $y$ salads is $1.5 x plus 1.9 y$ . It's given that the employee spends a total of $46.1$ minutes preparing $x$ sandwiches and $y$ salads. Thus, the equation $1.5 x + 1.9 y = 46.1$ represents this situation.

Choice A is incorrect. This equation represents a situation where it takes the employee $1.9$ minutes, rather than $1.5$ minutes, to prepare a sandwich and $1.5$ minutes, rather than $1.9$ minutes, to prepare a salad.

Choice C is incorrect. This equation represents a situation where it takes the employee $1$ minute, rather than $1.5$ minutes, to prepare a sandwich and $1$ minute, rather than $1.9$ minutes, to prepare a salad.

Choice D is incorrect. This equation represents a situation where it takes the employee $30.7$ minutes, rather than $1.5$ minutes, to prepare a sandwich and $24.3$ minutes, rather than $1.9$ minutes, to prepare a salad.