Question

supposed that there are two types of tickets to a show: Advance and same-day. Advance tickets cost $25 and same-day tickets cost $40.For one performance, there were 60 tickets sold in all, and the total amount paid for them was $205. How many tickets of each type were sold?number of advanced tickets sold:number of same-day tickets sold:

Answer 1

For the show there are two types of tickets:

Advance tickets, that cost $25

Same-day tickets, that cost $40

We know that for one function there were 60 tickets sold for a total amount of $205.

Let "a" represent the number of advanced tickets sold and "s" represent the number of same-day tickets sold.

The total number of tickets sold for the function can be expressed as the sum of the number of advance tickets (a) sold and the number of same-day tickets sold (s)

`60=a+s`

If each advance ticket costs $25 and there were "a" advance tickets sold, the total earnings for advance tickets can be expressed as 25a

And if each same-day ticket costs $40 and there were "s" same-day tickets sold, the earnings for selling same-day tickets can be expressed as 40s

The total earnings for the performance can be expressed as the sum of the earnings for selling advance tickets and the earnings for selling same-day tickets:

`205=25a+40s`

Both equations established form an equation system and we can use them to determine the number of advance and same-day tickets sold:

-First, write the first equation for one of the variables, I will write it for "a"

`\begin{gathered} 60=a+s \\ a=60-s \end{gathered}`

-Second, replace the expression obtained for "a" into the second equation:

`\begin{gathered} 205=25a+40s \\ 205=25(60-s)+40s \end{gathered}`

From this expression, we can calculate the value of "s", first, you have to distribute the multiplication on the parentheses term, which means that you have to multiply both terms by 25:

`\begin{gathered} 205=25\cdot60-25\cdot s+40s \\ 205=1500-25s+40s \end{gathered}`

Next, simplify the like terms

`205=1500+15s`

Pass "1500" to the other side by applying the inverse operation to both sides of it, which means that you have to subtract 1500 to both sides of the equal sign:

`\begin{gathered} 205-1500=1500-1500+15s \\ -1295=15s \end{gathered}`

And finally divide both sides by 15 to reach the value of s

`\begin{gathered} -(1295)/(15)=(15s)/(15) \\ -86.33=s \end{gathered}`

With the value of s calculated, you can replace it into the expression obtained for a and calculate its value:

`\begin{gathered} a=60-s \\ a=60-(-86.33) \\ a=146.33 \end{gathered}`

So with the information given, the number of advanced and same-day tickets sold are:

a=146.33

s=-86.33