The aquarium charges an entrance fee of $5 per child and $12 per adult. On one day, 100 people visited the aquarium. They collected $780 in admission fees. Which system of equations could be used to determine the number of adults that visited the aquarium? Let c represent the number of children and a represent the number of adults.

We set up 2 equations

A) C + A = 100

B) 5C + 12A = 780

We multiply A by -5

A) -5C -5A = -500   then we add B

B) 5C + 12A = 780

7A = 280

Number of Adults = 40

5C = 780 - 40*12

5C = 780 -480

5C = 300

Number of Children = 60

Step-by-step explanation:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.