Each school year, the seventh graders who study Life Science participate in a special field trip to the city zoo. In 2010, the school paid $1,260 for 84 students to enter the zoo. In 2011, the school paid $1,050 for 70 students to enter the zoo. In 2012, the school paid $1,395 for 93 students to enter the zoo. A. Is the price the school pays each year in entrance fees proportional to the number of students entering the zoo? Explain why or why not.

The price is proportional to number of students

Step-by-step explanation:

Given

2010: $1260 for 84 students

2011: $1050 for 70 students

2012: $1395 for 93 students

Required

Determine if the price is proportional to number of students

To do this, we simply divide the price by number of students in each year.

In 2010

In 2011

In 2012:

Notice that the ratio in the 3 years is 15.

Hence, the price is proportional to number of students

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

so what is the problem what are they asking you to solve

step-by-step explanation:

so what is the problem what are they asking you to solve