Question 203232
Let 

x = # of adult tickets sold


y = # of child tickets sold



Since "500 tickets were sold" total, this means that {{{x+y=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+5y=3475}}}






So we have the system of equations:



{{{system(x+y=500,8x+5y=3475)}}}



{{{x+y=500}}} Start with the first equation.



{{{y=500-x}}} Subtract {{{x}}} from both sides.



{{{y=-x+500}}} Rearrange the terms and simplify.



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{{{8x+5y=3475}}} Move onto the second equation.



{{{8x+5(-x+500)=3475}}} Now plug in {{{y=-x+500}}}.



{{{8x-5x+2500=3475}}} Distribute.



{{{3x+2500=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=(975)/(3)}}} 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+y=500}}} Go back to the first equation.



{{{325+y=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.