Question 894411: Tickets for a concert are $40 for main-floor seats and $25 for upper level seats. A total of 2000 concert tickets were sold. The total ticket sales were $62,000. How many main-floor tickets were sold and how many upper-level tickets were sold? You can solve this problem using two equations.
Answer by algebrapro18(249)   (Show Source):
You can put this solution on YOUR website! Lets let x be the number of tickets sold for main floor seats and let y be the number of tickets sold for upper level seats. We know that a total of 2000 concert tickets were sold so that means that x+y = 2000. We also know that ticket sales grossed $62,000. So we know that 40x+25y = 62,000. So we get the following system of equations:
x+y=2000
40x+25y = 62,000
There are different ways to solve this system. You can either graph the lines and see where they intersect, you can solve using elimination, or you can solve using substitution which is what I'm going to do.
To solve a system of equations you need to do the following:
1) Solve one equation for either x or y
2) Substitute the solution in step 1 into the other equation and solve for the other variable(if you solved for x in step 1 then solve for y in step 2 and vice versa).
3) Plug your solution from step two back into the equation found in step 1 and solve.
Doing so we get the following:
1)I'm going to solve the top equation for x.
x+y = 2000 subtract y from both sides
x = 2000-y
0
2)Plugging in and solving for y we get:
40x+25y = 62,000
40(2,000-y)+25y=62,000 Distribute
80,000-40y+25y=62,000 Combine Like Terms
80,000-15y=62,000 Subtract 80000 from both sides
-15y = -18,000 Divide both sides by -15
y = 1,200
3)Plugging in y=1,200 into the equation we found in step 1 we get:
x = 2000-y Plug in y =1,200
x = 2000 - 1200
x = 800
So we know that their were 800 main floor seat tickets and 1200 upper level seat tickets sold.
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