Answer:
Number of matinee tickets sold = 900
Number of student tickets sold = 1800
Number of regular tickets sold = 5800
Step-by-step explanation:
Given information
Total number of tickets sold = 8500
Total proceeds = $64,600
Cost of matinee admission = $5
Cost of student admission = $6
Cost of regular admission = $5
Student tickets sold are twice that of matinee admission
Now, let the matinee , student and regular admission are [tex]m[/tex], [tex]s[/tex], and [tex]r[/tex] respectively.
according to the given information we can say that
[tex]m+s+r=8500[/tex]
[tex]5m+6s+8.50r=8500[/tex]
as given in the question that Student tickets sold are twice that of matinee admission, so we can write
[tex]m+s+r=8500[/tex]
as, [tex]m+2m+r=8500\\[/tex]
[tex]3m+r=8500\\r=8500-3m\\[/tex]
Substituting the above value in equation
[tex]5m+6s+8.50r=8500[/tex]
And write as:
[tex]5m+6(2m)+8.50(8500-3m)=64600\\5m+12m+72250-25.50m=64600\\17m-25.50m=64600-72250\\-8.50m=-7650\\m=(-7650)/(-8.50)\\m=900[/tex]
As we have the value of [tex]m[/tex] so the value of [tex]r[/tex] and [tex]s[/tex] will be
[tex]r=8500-3m\\r=8500-(3*900)\\r=8500-2700\\r=5800[/tex]
and
[tex]m+s+r=8500\\900+s+5800=8500\\s=8500-6700\\s=1800\\[/tex]
Hence,
Number of matinee tickets sold = 900
Number of student tickets sold = 1800
Number of regular tickets sold = 5800
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