Mega Movies hosted a film premiere on Friday night. They charged $9 for adults and $5 for children. Ninety-seven adults and children attended, and $765 was made in ticket sales. How many children and how many adults went to the film premiere?

27 children, 70 adults

Step-by-step explanation:

Mega Movies hosted a film premiere on Friday and charged $9 for adults and $5 for children.

97 adults and children attended, and a total of $765 was made in ticket sales.

Let's represent adults with a

Let's represent children with c

a + c = 97 i

9a + 5c = 765 ii

Multiply equation I by 9

Multiply equation ii by 1

9a + 9c = 873 iii

9a + 5c = 765 iv

Subtract equation iv from iii

4c = 108

c = 108/4

c = 27

There are 27 children

From equation I

a + c = 97

a + 27 = 97

a = 97-27

a = 70

There are 70 adults

70 adults and 27 children went to the film premiere.

Step-by-step explanation:

Let's call the number of adults A, and the number of children C.

The total number of people were 97, so:

A + C = 97

The total earning was $765, so:

9A + 5C = 765

From the first equation:

A = 97 - C

using this value in the second equation:

9*(97 - C) + 5C = 765

873 - 9C + 5C = 765

4C = 108

C = 27

Then we find the value of A:

A = 97 - C = 97 - 27 = 70

70 adults and 27 children went to the film premiere.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: