Question

suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $35 and same-day tickets cost $40. One performance there was 60 tickets sold in all and the total amount paid for them was $2200. how many of each was sold?

Answer 1

Let the variable "x" represent the number of advanced tickets sold and variable "y" the amount of same-day tickets sold.

For a function there were a total of 60 tickets sold, between the advanced and the same- day tickets. You can express the total number of tickets sold as an equation with two unknowns:

`x+y=60`

Each "advanced" ticket costs $35, if x advanced tickets were sold, the total amount will be 35x

Each "same-day" ticket costs $40, for the y tickets sold, the total amunt will be 40y

If $2200 were collected in total, you can express the total amount earned as an equation with two unknowns:

`35x+40y=2200`

With this we have an equation system determined, now we can proceed to solve it:

Step 1, write the first equation in terms of one of the variables.

I'll do it for x:

`\begin{gathered} x+y=60 \\ x=60-y \end{gathered}`

Stept 2, replace the expression of step 1 in the second equation:

`35(60-y)+40y=2200`

Now you can solve for y. First solve the term in parentheses by applying the distributive propperty of multiplications:

`\begin{gathered} 35\cdot60-35\cdot y+40y=2200 \\ 2100-35y+40y=2200 \end{gathered}`

Next pass the number to the left side and add both y-related terms:

`\begin{gathered} 5y=2200-2100 \\ 5y=100 \end{gathered}`

Finally divide both sides by 5 to determine the amount of "same-day" tickets sold:

`\begin{gathered} (5y)/(5)=(100)/(5) \\ y=25 \end{gathered}`

Now that you know the value of y, replace it in the first formula to determine the value of x

`\begin{gathered} x=60-y \\ x=60-25 \\ x=35 \end{gathered}`

So, there were sold 35 tickets in advance and 25 same-day tickets.