Pa carnival sold tickets for $1.50 for adults and $1.00 for students. there were 54 tickets sold for a total of $70.50. write a system of equations to represent the number of adult tickets, x, and the number of student tickets, y. find the solution and explain what it means?

Step-by-step explanation:

For such problems, it is convenient to write one equation for the total number of tickets sold

  x + y = 54

and another equation for the total revenue collected from the sales

  1.50x + 1.00y = 70.50

These equations are conveniently solved by eliminating the variable representing the lowest-price tickets (y). Here, we can simply subtract the first equation from the second:

  (1.50x +1.00y) -(x + y) = (70.50) -(54)

  0.50x = 16.50 . . . . simplify

  x = 33 . . . . . . . . . . . multiply by 2

  y = 54 -x = 21 . . . . . find the value of y

Given the definitions of the variables, (x, y) = (33, 21) means 33 adult ticket and 21 student tickets were sold.

step-by-step explanation:

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!