Question

Aaliyah is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges $47 for the meal, plus $3 per pound for the lobster she picks. At the second restaurant, Aaliyah would pay $4 per pound for the lobster, in addition to $27 for the meal. Aaliyah realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. What is the weight? How much would Aaliyah pay for her dinner?

Answer 1

By setting up an equation for each restaurant's pricing structure and finding where they are equal, we can determine that Aaliyah would need a lobster that weighs 20 pounds for the dinner costs to be the same at $107 at both restaurants.

Step-by-step explanation:

To find the weight of lobster at which the cost of dinner at both restaurants is the same, we establish an equation where the total cost at the first restaurant equals the total cost at the second restaurant.

Let x be the weight of the lobster in pounds. The cost at the first restaurant is $47 (flat rate) plus $3 per pound of lobster, so the cost equation is 47 + 3x. At the second restaurant, the cost is $27 (flat rate) plus $4 per pound, giving us the cost equation 27 + 4x.

We set these two equations equal to each other to find the weight where the costs are the same:

• 47 + 3x = 27 + 4x
• 20 = x

So, if the lobster weighs 20 pounds, the cost of the dinner would be the same at both restaurants.

To calculate the total cost, we simply substitute x with 20 pounds:

First restaurant: 47 + 3(20) = 47 + 60

= $107

Second restaurant: 27 + 4(20) = 27 + 80

= $107

Therefore, for a 20-pound lobster, Aaliyah would pay $107 for her dinner at either restaurant.