Graph the function of total cost for each venue, and see for what value of x Maple Ridge's function lies below the other two.
More than 100.
Practice makes perfect
To start, we need a function rule for the total cost at Maple Ridge. We know that they charge $ 10 per student plus a rental fee.
y= 10x+b
We also know that they charge a total of $1 900 for 140 students. If we substitute these values for y and x respectively, we will get the value of b to finish our function.
Now we can complete the function rule for the total cost at Maple Ridge.
y=10x+500
Since we know the function rules for the total cost at Sunview Resort, y=10x+600 ,and Lakeside Inn, 12x+300, we can graph them all in the coordinate plane.
Because the functions for Sunview Resort and Maple Ridge have the same slope and Sunview has a bigger y-intercept, the price at Maple Ridge is always lower. We can see on the graph that these function are parallel, and the function for Maple Ridge always lies below.
10x+500< 10x+600
In order to find the number of students for Maple Ridge to be cheaper than Lakeside Inn, we have to solve the following inequality.
f_M(x)< f_L(x)
Here f_M(x) is the function for Maple Ridge and f_L(x) is the function for Lakeside Inn.
In the context of the word problem, this means that more than 100 students have to attend for Maple Ridge to be the cheapest option. On the graph, we can see that for x>100 Maple Ridge's function lies below Lakeside Inn's function.
