Question

You are organizing a class trip to an amusement park. The cost to enter the park is $30. The cost to enter with the meal plan is $45. You have a budget of $2700 for the trip. The equation 30x + 45y = 2700 model the total cost for the class to go on the trip, where x is the number of students who do not choose the meal plan and y is the number of students who do choose the meal plan. The graph below also models the equation.a.) In your own words, interpret the meaning of the y-intercept.b.) If 60 students do not choose the meal plan, how many students did choose the meal plan?

Answer 1

Given :

The cost to enter the park is $30.

The cost to enter with the meal plan is $45.

Total budget = $2700

The model of the total cost : 30x + 45y = 2700

x : is the number of the students who do not choose the meal plan

y : is the number of students who do choose the meal plan.

And the following graph represents the model of equation

a) As shown in the figure : y - intercept is the point ( 0 , 60 )

The y- intercept is the point at which x = 0

So, when x = 0 , y = 60

Which mean : the total number of the students at this case = 60 students

And all of them choose the meal plane

As the budget = $2700, the minimum number of the students can go the trip is 60

b) if 60 students do not choose meal plane , how many students did choose the meal plane?

60 students do no choose the meal plane. so, x = 60

To find the students who choose the meal plane, substitute with x = 60 at the give equation

`\begin{gathered} 30\cdot60+45y=2700 \\ 1800+45y=2700 \\ 45y=2700-1800 \\ 45y=900 \\ \\ y=(900)/(45)=20 \end{gathered}`

OR can be calculated using the graph ,

at x = 60 , go up till the intersection with the line then go left to find the corresponding value of y as shown in the following figure :

So, y = 20

The answer is : the number of the students who choose the meal plane = 20 students