A study of 80 pupils was conducted on the modes of transportation when they travel back to their hometowns, 25 pupils travel by train and 48 pupils travel by train or car. If 7 pupils travel by train and car, 5 pupils travel by bus and train, and 2 pupils travel by all three modes of transportation, how many pupils do travel by bus or train but not by car? Only for genius.​

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!

3x + 4y -25 =0 represents the amount of change sianna should recieve

it would take 7/10 of an hour too fill the pool.

step-by-step explanation: