SOLUTION: I'm having problems working out two sections in this problem. The Graph shows the tickets available over a two day period at The University of Florida's Stadium. Let x represent

Question 1080883: I'm having problems working out two sections in this problem.
The Graph shows the tickets available over a two day period at The University of Florida's Stadium. Let x represent the time in hours and y represent the numbers of seats available. The graph shows the x-intercept at (18,0) and the Y-intercept at(0,90,000)
The questions I'm having problems with is part (c). From the graph, determine how many seats remain after 16 hours and part (d). determine how long it takes to sell the first 20,000 available seats.
Found 2 solutions by Theo, Boreal:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x-intercept is (18,0)
y-intercept is (0,90,000)

the slope is equal to (y2-y1)/(x2-x1)

if (x1,y1) = (18,0) and (x2,y2) = 0,90,000, then the slope is equal to (90,000-0) /(0-18) = 90,000/-18 = -5000.

the general form of a straight line equation is y = mx + b

m is the slope
b is the y-intercept

your equation becomes y = -5000 * x + b

replace x and y with the value of one of the points.

try (x1,y1) = (18,0)

the formuila becomes 0 = -5000 * 18 + b

solve for b to get b = 90,000

that should have been obvious because one of the points was the y-intercept.

stupid of me but i got the right answer anyway.

the equation becomes y = -5000 * x + 90,000

the graph shows the tickets available.

presumably, as tickets are sold, the number of available tickets becomes less.

after 18 hours, all the tickets are sold and there are no more tickets available.

that says that 90,000 tickets were sold in 18 hours.

the first question is how many tickets remain after 16 hours.

the equation of y = 90,000 - 5000 * x becomes y = 90,000 - 5000 * 16 which becomes y = 90,000 - 80,000 which becomes y = 10,000.

that means there are 10,000 tickets left after 16 hours.

the next question is how long does it take to sell the first 20,000 available seats.

since 5000 tickets are sold every hour, this means that the first 20,000 tickets were sold in 4 hours.

the graph looks like this:

you can see that, after 4 hours, 70,000 tickets are left, which means that 20,000 have been sold.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Two points can give one the slope
Change in y is 90000, change in x is -18; slope=-5000
point slope formula y-y1=m(x-x1), m slope, x1,y1 point
y=-5000(x-18)=-5000x+90000
Want when y=70,000, since this represents number of available seats when 20,000 have been sold.
70000=-5000x+90000
-20000=-5000x
x=4 hours. 5000 seats are sold per hour.
After 16 hours, 10,000 seats are left (5000*16)=80000.
or y=-5000(16-18)=-5000(-2)=10000

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