Question

Betty is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges $25 for the meal, plus $3 per kilogram for the lobster she picks. At the second restaurant, Betty would pay $2 per kilogram for the lobster, in addition to $30 for the meal. Betty realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. What is the weight?

Answer 1

Betty would pay the same cost for a lobster dinner at both restaurants if the lobster weighs 5 kilograms, as determined by setting up and solving the equation 25 + 3x = 30 + 2x.

Step-by-step explanation:

To find the weight of the lobster at which the cost of dinner at both restaurants would be the same, we need to set up an equation where the total costs for each restaurant are equal. At the first restaurant, the cost is $25 for the meal plus $3 per kilogram for the lobster. At the second restaurant, the cost is $30 for the meal plus $2 per kilogram for the lobster. Let x be the weight of the lobster in kilograms.

The equation for the cost at the first restaurant is 25 + 3x and for the second restaurant it is 30 + 2x. To find the weight where both costs are equal, we set the equations equal to each other: 25 + 3x = 30 + 2x. Solving this equation for x, we subtract 2x from both sides to get x = 5.

Thus, Betty would pay the same cost for a lobster dinner at both restaurants if the lobster weighs 5 kilograms.