Question

ted is comparing the cost of a fresh lobster dinner at two different restaurants. the first restaurant charges $30 for the meal, plus $3 per kilogram for the lobster he picks. at the second restaurant, ted would pay $2 per kilogram for the lobster, in addition to $50 for the meal. ted realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. how much would ted pay for his dinner? write a system of equations, graph them, and type the solution.

Explanation:

Step1: Define the variables

Let \(x\) be the weight of the lobster (in kilograms) and \(y\) be the total cost of the dinner.
For the first restaurant: \(y = 3x+30\)
For the second restaurant: \(y = 2x + 50\)

Step2: Solve the system of equations

Set the two equations equal to each other:

$$
LATEXBLOCK0
$$

Step3: Find the value of \(y\)

Substitute \(x = 20\) into one of the equations. Let's use \(y=3x + 30\)

$$
LATEXBLOCK1
$$

Answer:

The system of equations is \(

$$\begin{cases}y = 3x+30\\y=2x + 50\end{cases}$$

\). The solution is \((20,90)\), meaning when the lobster weighs \(20\) kilograms, Ted would pay \(\$90\) for his dinner.