Agroup of friends is collecting aluminum for a recycling drive. each person who donates at least 4.25 pounds of aluminum receives a free movie coupon. the weight of each person's donation is shown in the table. a. order the weights of the donations from greatest to least. b. which of the friends will receive a free movie coupon? which will not? c. what if? would the person with the smallest donation win a movie coupon if he or she had collected 1/2 pound more of aluminum? explainbrenda. claire jim. micah4.3. 5.5. 6 1/6. 15/4peter4 3/8

Brenda      Claire      Jim     Micah        Peter

 4.3             5.5       6 1/6     15/4           4 3/8

 4.3             5.5       6.17      3.75        4.375   (all values in decimal)

A. order the weights of the donations from greatest to least.

6.17 , 5.5 , 4.375 , 4.3 , 3.75

B. Which of the friends will receive a free movie coupon? Which will not?

As given - Each person who donates at least 4.25 pounds of aluminum receives a free movie coupon.

So, Brenda, Claire, Jim and Peter will receive coupons and Micah will not receive.

C.What if? Would the person with the smallest donation win a movie coupon if he or she had collected 1/2 pound more of aluminum?

Micah got 3.75 pounds and if he got 0.5 pounds more, then he would have;

pounds

Then he would have got the coupon as a minimum of 4.25 pounds is required.

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!