SOLUTION: adult ticket prices are 8 dollars kid ticket prices are 5 dollars if 500 tickets were sold and the total amount of the tickets equals 3475 dollars, how do i find how many adult and

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Question 203232: adult ticket prices are 8 dollars kid ticket prices are 5 dollars if 500 tickets were sold and the total amount of the tickets equals 3475 dollars, how do i find how many adult and child ticket prices were sold?
I got the answer I came up with 325 adults, and 175 kids, but HOW do I show the work, how do I set up the equation. it was on my job interview today... i felt really stupid
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let
x = # of adult tickets sold

y = # of child tickets sold


Since "500 tickets were sold" total, this means that x%2By=500


Also, because "adult ticket prices are 8 dollars kid ticket prices are 5 dollars", and "the total amount of the tickets equals 3475 dollars", we get the second equation 8x%2B5y=3475





So we have the system of equations:


system%28x%2By=500%2C8x%2B5y=3475%29


x%2By=500 Start with the first equation.


y=500-x Subtract x from both sides.


y=-x%2B500 Rearrange the terms and simplify.


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8x%2B5y=3475 Move onto the second equation.


8x%2B5%28-x%2B500%29=3475 Now plug in y=-x%2B500.


8x-5x%2B2500=3475 Distribute.


3x%2B2500=3475 Combine like terms on the left side.


3x=3475-2500 Subtract 2500 from both sides.


3x=975 Combine like terms on the right side.


x=%28975%29%2F%283%29 Divide both sides by 3 to isolate x.


x=325 Reduce.


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Since we know that x=325, we can use this to find y.


x%2By=500 Go back to the first equation.


325%2By=500 Plug in x=325.


y=500-325 Subtract 325 from both sides.


y=175 Combine like terms on the right side.


So the solutions are x=325 and y=175.


This means that 325 adult tickets and 175 child tickets were sold.