A school spent $150 on advertising for a breakfast fundraiser. Each plate of food was sold for $8.00 but cost the school $2.00 to prepare. After all expenses were paid, the school raised $2,400 at the fundraiser. Which equation can be used to find x, the number of plates that were sold?

6x – 150 = 2,400
6x + 150 = 2,400
10x – 150 = 2,400
10x + 150 = 2,400

6x-150 = 2400

Given: The selling price of each plate = $8.00

The cost of plate to prepare = $2.00

Let x be the  number of plates that were sold

Then, the profit amount raised by school is given by

The amount spent by school on advertising for a breakfast fundraiser= $150

The final amount raised by school = $2,400

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!