Question 1162085
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Let x be the number of adult tickets.

Then the number of the kid tickets is (79-x).


You then write this money equation for the total


    7*x + 4.50*(79-x) = 428   dollars.


From the equation,  x = {{{(428-4.50*79)/(7-4.50)}}} = 29.


<U>ANSWER</U>.  29 adult tickets and the rest,  79-29 = 50 kid tickets.


<U>CHECK</U>.  29*7 + 50*4.50 = 428 dollars.   ! Precisely correct !
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Solved.