A theater has a revenue of 36,600 while selling 4200 tickets total. An adults ticket costs 10 dollars and a child's ticket costs 5.5 dollars. How many tickets in total did the sell of each.

they sold 3000 adult tickets and 1200 children tickets.

Step-by-step explanation:

Let x represent the number of adult tickets that they sold.

Let y represent the number of children tickets that they sold.

The theatre sold a total of 4200 tickets. This means that

x + y = 4200

An adults ticket costs 10 dollars and a child's ticket costs 5.5 dollars. The

theater had a revenue of 36,600. This means that

10x + 5.5y = 36600- - - - - - - - -- -1

Substituting x = 4200 - y into equation 1, it becomes

10(4200 - y) + 5.5y = 36600

42000 - 10y + 5.5y = 36600

- 10x + 5.5y = 36600 - 42000

- 4.5y = - 5400

y = - 5400/ - 4.5

y = 1200

x = 4200 - y = 4200- 1200

x = 3000

step-by-step explanation:

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)