Mega Movies hosted a film premiere on Friday night. They charged $9 for adults and $4 for children. One hundred fifty-eight adults and children attended, and $1,352 was made in ticket sales. How many children and how many adults went to the film premiere?
A.
18 children; 140 adults
B.
8 children; 150 adults
C.
14 children; 144 adults
D.
11 children; 147 adults

C.

14 children; 144 adults

Step-by-step explanation:

This question can be solved by a system of equations.

I am going to say that:

x is the number of children who went to the film premiere

y is the number of adults who went to the film premiere.

One hundred fifty-eight adults and children attended

This means that

They charged $9 for adults and $4 for children. $1,352 was made in ticket sales.

This means that

So

From the first equation

Replacing in the second equation

So the correct answer is:

C.

14 children; 144 adults

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!