SOLUTION: Thank you so much. These are homework problems, and I am a straight-A student. I am not trying to be cheap, I just seriously don't understand it. I have tutoring tomorrow, and need

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Thank you so much. These are homework problems, and I am a straight-A student. I am not trying to be cheap, I just seriously don't understand it. I have tutoring tomorrow, and need      Log On


   

Question 750473: Thank you so much. These are homework problems, and I am a straight-A student. I am not trying to be cheap, I just seriously don't understand it. I have tutoring tomorrow, and need to know how to do these by then. Thanks for your help. It is greatly appreciated! :)
1. The junior prom committee brought in $6300 through ticket sales last year. This year they
had hoped to increase attendance by lowering the ticket price by $3. They ended up selling 48 more tickets for a total of $5970.
a. What was the original price per ticket?
b. How many tickets were sold at the lower price?
2. When Raj shined his flashlight on the wall at an angle, it made an ellipse with a vertical major axis of 34 inches and a horizontal minor axis of 18 inches. Let the center of the ellipse be the origin of a coordinate system. Find an equation for the edge of the ellipse.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1. The junior prom committee brought in $6300 through ticket sales last year. This year they
had hoped to increase attendance by lowering the ticket price by $3. They ended up selling 48 more tickets for a total of $5970.
a. What was the original price per ticket?
h = # of tix at higher price
p = higher price
h*p = 6300
(h+48)*(p-3) = 5970
h = 6300/p
(6300/p + 48)*(p-3) = 5970
(6300 + 48p)*(p-3) = 5970p
(2100 + 16p)*(p-3) = 1990p
16p^2 + 2052p - 6300 = 1990p
8p^2 + 31p - 3150 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 8x%5E2%2B31x%2B-3150+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2831%29%5E2-4%2A8%2A-3150=101761.

Discriminant d=101761 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-31%2B-sqrt%28+101761+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2831%29%2Bsqrt%28+101761+%29%29%2F2%5C8+=+18
x%5B2%5D+=+%28-%2831%29-sqrt%28+101761+%29%29%2F2%5C8+=+-21.875

Quadratic expression 8x%5E2%2B31x%2B-3150 can be factored:
8x%5E2%2B31x%2B-3150+=+%28x-18%29%2A%28x--21.875%29
Again, the answer is: 18, -21.875. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B31%2Ax%2B-3150+%29

==========================
p = $18 (original price)
==========================
b. How many tickets were sold at the lower price?
Tix at $18 = 6300/18 = 350
350 + 48 = 398 at the lower price
==================
2. When Raj shined his flashlight on the wall at an angle, it made an ellipse with a vertical major axis of 34 inches and a horizontal minor axis of 18 inches. Let the center of the ellipse be the origin of a coordinate system. Find an equation for the edge of the ellipse.
---------
18/2 = 9
34/2 = 17
------
x%5E2%2F9%5E2+%2B+y%5E2%2F17%5E2+=+1
x%5E2%2F81+%2B+y%5E2%2F289+=+1