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Algebra / Linear equations in one variable Difficulty: Medium

The cost to rent a commercial fishing boat from a certain company is $dollar sign 950$ for the first $2$ hours and an additional $dollar sign 50$ per hour for each hour after the first $2$ hours. If the total cost to rent the commercial fishing boat from the company for $t$ hours, where $t greater than 2$ , is $dollar sign 1,100$ , which equation represents this situation?

$950 (t - 2) + 50 t = 1,100$

$950 (2 t) + 50 t = 1,100$

$950 + 50 (t - 2) = 1,100$

$950 + 50 (2 t) = 1,100$

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Explanation

Choice C is correct. It’s given that the cost to rent a commercial fishing boat is $dollar sign 950$ for the first $2$ hours and an additional $dollar sign 50$ per hour for each hour after the first $2$ hours. It’s also given that $t$ represents the total number of hours and $t greater than 2$ . Therefore, the number of additional hours after the first $2$ hours can be represented with the expression $t minus 2$ . The cost for these additional hours is $dollar sign 50$ per hour, so the cost for the additional hours can be represented by the expression $50 left parenthesis t minus 2 right parenthesis$ . The total cost can be calculated by adding the cost for the first $2$ hours to the cost for the additional hours and can be represented by the expression $950 + 50 (t - 2)$ . It’s also given that the total cost to rent the commercial fishing boat from the company for $t$ hours is $dollar sign 1,100$ . Thus, the equation that represents this situation is $950 + 50 (t - 2) = 1,100$ .

Choice A is incorrect and may result from conceptual errors.

Choice B is incorrect and may result from conceptual errors.

Choice D is incorrect and may result from conceptual errors.