Question

The number of tickets for sale at $28 should be…The number of tickets for sale at $40 should be…

Answer 1

Let's call x the number of $28's tickets sold and y the number of $40's tickets sold.

The total number of seats is 5000 then:

`x+y=5000\text{ Eq.(1)}`

To generate total revenue of $161,600 the tickets sold must be:

`x\cdot28+y\cdot40=161,600\text{ Eq.(2)}`

In equation 1, solve for x:

`x=5000-y\text{ Eq.(3)}`

Now, replace this into equation 2:

`(5000-y)\cdot28+y\cdot40=161,600`

Solve for y:

`\begin{gathered} \text{Apply the distributive property} \\ 5000\cdot28-y\cdot28+y\cdot40=161,600 \\ 140,000+12y=161,600 \\ \text{Subtract 140000 from both sides} \\ 140,000+12y-140,000=161,600-140,000 \\ 12y=21600 \\ y=(21600)/(12) \\ y=1800 \end{gathered}`

Replace the y-value into equation 3 and find x:

`\begin{gathered} x=5000-1800 \\ x=3200 \end{gathered}`

Now let's check by replacing both values into equation 2:

`\begin{gathered} 3200\cdot28+1800\cdot40=161,600\text{ Eq.(2)} \\ 89600+72000=161,600 \\ 161,600=161,600\text{ O.K.} \end{gathered}`

Answer:

The number of tickets for sale at $28 should be 3200.

The number of tickets for sale at $40 should be 1800.