Question

Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $60. Forone performance, 25 advance tickets and 40 same-day tickets were sold. The total amount paid for the tickets was $2025. What was the price of each kind ofticket?Note that the ALEKS graphing calculator can be used to make computations easier.x5?Advance ticket: 50Same-day ticket: s8M

Answer 1

Let 'x' represents the advance ticket,

Let 'y' represents the same-day ticket.

Therefore,

The combined cost of one advance ticket and the same ticket is $60, and it can be represented mathematically below.

`x+y=\text{ \$60}\ldots\ldots.(1)`

Secondly, the sum of 25 advance tickets and 40 same-day tickets is $2025. Mathematically,

`25x+40y=\text{ \$2025}\ldots\ldots..(2)`

Let us now combine the equations together,

`\begin{gathered} x+y=\text{ \$60}\ldots\ldots\ldots\ldots1 \\ 25x+40y=\text{ \$2025}\ldots\ldots\ldots.2 \end{gathered}`

Let us make x the subject of the formula in equation (1),

`x=\text{ \$60-y}\ldots\ldots..(3)`

Now let us substitute the 'x' into equation (2), and solve for y.

`25(\text{ \$60-y)+40y=\$2025}`
`\text{ \$1500-25y+40y=\$2025}`
`\begin{gathered} \text{ \$1500+15y=\$2025} \\ \text{collect like terms,} \\ 15y=\text{ \$2025-\$1500} \end{gathered}`
`\begin{gathered} 15y=525 \\ y=(525)/(15) \\ y=\text{ \$35} \end{gathered}`

Let us now substitute the value of y into equation 3 to solve for x,

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

Hence, Advance ticket is $25,

Same-day ticket is $35.