A high school musical production sells student tickets for $5 each and adult tickets for $8 each. If the ratio of adult to student tickets purchases is 3:1, what is the average income per ticket sold?

Answer 1

(8 + 8 + 8 + 5) / 4 = ?

Answer 2

If the ratio of adult to student tickets sold is 3:1, that means 3 adult tickets are sold for every 1 student ticket. So, out of every 4 tickets sold, 3 are adult tickets. This means that adult tickets make up 75% of sales and student tickets made up 25%. If we represent the average price of all tickets with those proportions, we can form the expression: $8*.75 + $5*.25 = $6 + $1.25 = $7.25 on average.

More intuitively, we could look at the average revenue earned from the sale of 4 tickets: 3 adult tickets, 1 student ticket, per the ratio. 3 adult tickets would equal 3*$8 = $24 and 1 student ticket would equal 1*$5. In total, that is $29 for 4 tickets. If we divide $29/4, we get the same answer as above, an average of $7.25/ticket.

Answer 3

Interesting problem. The average income per ticket sold would be the total income divided by the total number of tickets sold.

The total income is the number of student tickets sold times $5 plus the number of adult tickets sold times $8. So if we let "s" be the number of student tickets sold, then, because the ratio is 3:1, the number of adult tickets sold must be "3s"

So the total income would be 5s + (3s)(8) which equals 5s + 24s or 29s. The total number of tickets sold would be s + (3s) or 4s.

So the average income per ticket sold is 29s/4s = 29/4 = $7.25