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a theater audience of 90 people consists of adults,seniors,and students. The ticket prices are $9 for adults, $5 for seniors, and $2 for students. The total number of tickets sold to seniors and students is 20 more than the number of tickets sold to adults. The total money taken in from ticket sales is $515. How many adults, seniors and students are in attendance?
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Let a= number of adult tickets
Let s= number of seniors
then 90-a-s = number of students.
We are also given that: s + 90 -a -s = 20+a or 90 - a =20 + a. which is 2a=70
solving for a. a=35
That sets up the number of attendees, now lets do the money.
9a + 5s +2(90-a-s) = 515 (dollars)
9a + 5s + 180 -2a - 2s = 5i5 substituting 35 for a gets us.
315 + 5s + 180 - 70 = 515
5s=515 + 70 - 180 -315
5s = 90
there are 18 seniors
students = 90-a-18=72-a=72-35=37
adults = 35
sum of senior and students = 37 + 18 = 55
minus students 55-35 = 20 checks with the problem information given