Number of tickets sold to adults: 575
Number of tickets sold to students: 675
Step-by-step explanation:
To solve the problem, let's call:
A = the number of adults
S = the number of students
We know that the total attendance was 1250, so:
[tex]A+S=1250[/tex] (1)
Also we know that the cost of ticket was:
$6.00 per student
$7.50 per adult
And the total revenue was $8362.50
So we can write:
[tex]6.00S+7.50A=8362.50[/tex] (2)
Where [tex]6.00S[/tex] represents the revenue from students and [tex]7.50A[/tex] the revenue from adults.
So we have two equations in two variables, A and S. Multiplying eq.(1) by 6 we get
[tex]6A+6S=7500[/tex]
Dividing eq.(2) by this last equation, we get
[tex]1.50A=862.5[/tex]
From which we find
[tex]A=\frac{862.5}{1.50}=575[/tex]
And substituting into eq.(1),
[tex]575+S=1250\\S=1250-575=675[/tex]
Therefore:
Number of tickets sold to adults: 575
Number of tickets sold to students: 675
Learn more about systems of equations:
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