Tickets for a concert cost $35 for balcony seats and $75 for floor seats. Tickets at the same venue for a theatrical production
2 answers:
Answer:
systems of equations by elimination and manipulation.
Step-by-step explanation:
The systems of equations by elimination and manipulation method will help in this case find the number of seats there are in the theater.
We first need to create the equations.
Let x = number of balcony seats
Let y = floor seats
The equation for the concert will be:
35x + 75y = 27,750
The equation for the theatrical productions will be:
25x + 60y = 21,750
Now that we have our equations. Let's find a way to manipulate them to find the value of x and y.
35x + 75y = 27,750
25x + 60y = 21,750
In this case we need to find a way to eliminate either the x or y value by multiplying the equations with certain numbers.
Let's start by solving for x:
We can do this by multiplying the first equation by 4 and the second one by 5
4(35x + 75y = 27,750)
5(25x + 60y = 21,750)
Our new equations will be:
140x + 300y = 111,000
125x + 300y = 108,750
Now we can see the 300y on both equations can be eliminated if we subtract both equations to each other.
140x + 300y = 111,000
<u>-125x + 300y = 108,750</u>
15x + 0 = 2,250
x = 150
Now that we have the value for x, we can then insert the value to any of the formulas that we created to find the value of y.
Let's use the equation 25x + 60y = 21,750.
25(150) + 60y = 21,750
3,750 + 60y = 21,750
60y = 21,750 + 3,750
y = 425
So we have 150 Balcony seats and 425 Floor seats.
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