The total number N in thousands of inmates in state and fede

The total number (N in thousands) of inmates in state and federal prisons is given by the mathematical mode N = 7.6x + 115 where x stands for the number of years since 1990. Determine the following: Slope: Explain the meaning of the slope relative to the situation: y-intercept: Explain the meaning of the y-intercept relative to the situation: A concert promoter has 2, 400 tickets to sell. If the promoter charges $30 for arena seating and $45 for floor seating, how many tickets of each type must be sold in order for the total ticket revenue to reach $84,000? Write a system of equations in two variables that best describes the situation. Then solve you system of equations.

Solution

31. the genearal linear equation is written as y=mx+c where m is the slope and c is the y intercept. So comparing this equation with the given equation we get that the slope is 7.6. Here this 7.6 means that for every unit change in x the value of inmates will change by 7.6 times.

and the y intercept here is 115 which means that the starting value of inmates is 115 when we started to count or after 1990.

32. let the number of arena tickets sold be x and floor tickets be y.

so the total revenue would be 30x+45y

The total number of tickets is 2400

so

x+y=2400

30x+45y=84000

2x+3y=5600

subtracting 2 times first equation from second we get

y=800

x=2400-800

x=1600

so 1600 arena seating tickets and 800 floor seating tickets must be sold