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The price of one ticket is $ 62.2
<h3><u>Solution:</u></h3>Given that a performer expects to sell 5000 tickets for an upcoming event
They want to make a total of $ 311, 000 in sales from these tickets
<em><u>To find: price of one ticket</u></em>
Let us assume that all tickets have the same price
Let "a" be the price of one ticket
So the total sales price of $ 311, 000 is obtained from product of 5000 tickets and price of one ticket
Thus the price of one ticket is $ 62.2
Answer:
The solution to the system is the pair (9, 6)
Step-by-step explanation:
Hi!
First, let´s write the system of equations:
-y² + 6y + x -9 = 0
6y = x +27
The solutions of the system are the pairs (x, y) that satisfy both equations.
Let´s take the second equation and solve it for x:
6y = x +27
Subtract 27 from both sides of the equation
6y - 27 = x
Now, we can replace x in the first equation and solve it for y:
-y² + 6y + x -9 = 0
-y² + 6y + 6y - 27 -9 = 0
-y² + 12y - 36 = 0
Notice that -y² + 12y - 36 = -(y - 6)², then:
-(y - 6)² = 0
y - 6 = 0
y = 6
(alternatively you can solve the quadratic equation using the quadratic formula).
Now let´s find the value of x:
x = 6y -27
x = 6·6 -27
x = 9
The solution to the system is the pair (9, 6)
Please see the attached figure. The point where the curves intersect is the solution to the system.
