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 range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.