Question

ent Assignmen... Dashboard | Khan... Untitled document - Solid SLUOTES LOILTOTT RecomTTTTETNauuS Skupials 19 Language alls You have prizes to revea Eighth grade AA.3 Solve a system of equations by graphing: word problems W9J Christine is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges $30 for the meal, plus $3 per pound for the lobster she picks. At the second restaurant, Christine would pay $2 per pound for the lobster, in addition to $50 for the meal. Christine realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. How much would Christine pay for her dinner? Write a system of equations, graph them, and type the solution.

Answer 1

Let x represent the weight of lobster in the meal for which the cost of dinner in both restaurants would be the same.

For the first restaurant, they charge $30 for the meal, plus $3 per pound for the lobster she picks. This means that if she picks x pounds of lobster at this restaurant, the cost of the dinner would be

30 + 3x

For the second restaurant, they charge $50 for the meal, plus $2 per pound for the lobster she picks. This means that if she picks x pounds of lobster at this restaurant, the cost of the dinner would be

50 + 2x

The system of equations are

y = 30 + 3x

y = 50 + 2x

y represents the cost of the dinner

Given that when she picks x pounds of lobster, the cost would be the same, it means that

50 + 2x = 30 + 3x

3x - 2x = 50 - 30

x = 20

The amount that Christin would pay for her dinner is

30 + 3 * 20

= 30 + 60

= 90

She would pay $90 for the meal.

The graph is shown below

The blue line represents y = 50 + 2x

The red line represents y = 30 + 3x

At the point of intersection, the solution is (20, 90)