Tickets sales to the local gaming convention, playercon, are on the rise! sales of 2-day tickets brought in $188,100. a total of 6,600 tickets were sold. adult 2-day tickets cost $36.00 and children’s 2-day tickets cost $26.00. how many of each kind of ticket were sold?

Using numerical reasoning

Sale of 6600 children's tickets would provide revenue of ...

... 6600×$26 = $171,600

Revenue was actually $188,100 -171,600 = $16,500 more than that. Each adult ticket sold instead of a children's ticket increases revenue by $36 -26 = $10, so there were $16,500/$10 = 1650 adult ticket sold.

The number of children's tickets was then 6600 -1650 = 4950.

Using an equation

Let "a" represent the number of adult tickets sold. Then the number of children's tickets is (6600-a) and the total revenue is ...

... 36a +26(6600 -a) = 188,100

... 10a = (188,100 -171,600) . . . . . . . collect terms, subtract 26·6600

... 16,500/10 = a = 1650 . . . . . . . . . divide by the coefficient of "a"

... (6600 -a) = 6600 -1650 = 4950 . . . . . childrens's tickets sold.

There were 1650 adult and 4950 children's tickets sold.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

total of apples - take away four

6-4 = 2

answer is 2 apples