(3 pt)
which number sentences show ways to solve the problem?

the 9 members of a conservation club purchased a total of 45 tree saplings. each member bought the same number of trees to plant in the community. each tree cost $15. how much did each member pay for the trees?

choose all answers that are correct.

a.
15 × 9 = 135 and 135 – 75 = 60

b.
3 × 15 = 45 and 45 + 15 = 60

c.
45 ÷ 9 = 5 and 5 × 15 = 75

d.
45 × 15 = 675 and 675 ÷ 9 = 75

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!

you have 6 cupcakes