CCSS.HSA1SLE-QU.3 - Matt is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges $30 for the meal, plus $1 per kilogram for the lobster he picks. At the second restaurant, Matt would pay $2 per kilogram for the lobster, in addition to $15 for the meal. Matt realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. What is the weight? Write a system of equations, graph them, and type the solution.

Sangeetha Pulapaka (last edited 2 years ago) (Expert, Educator @Qalaxia)

STEP 1: Start by writing a system of equations. Let x=kilograms and y=dollars.

then we get the first equation as y=x+30 and the second equation as y=2x+15

The first equation is y=x+30.

STEP 2: Recall how to plot a set of equations on the coordinate axis

In the second equation,

The y-intercept is 30. Plot the point (0,30).

The x-intercept is -30. Plot the point (-30,0)

Take the first equation

y = 2x + 15

Now plot the x- and the y-intercepts for this equation

Plugging in x = 0 we get y = 15

Plugging in y = 0 we get x = \frac{-15}{2} = -7.5

Plot (0,15) and (-7.5,0) on the coordinate axis

You fill find the point of intersection to be (15,45). This is the solution.