Question

a music festival sold two types of ticket, day passes and weekend passes. The day passes were 105$ and the weekend passes was $111 the total ticket sale for the festival were 504,081$. they sold 201 more day passes than weekend passes. How many day passes and how many weekend passes were sold?they sold _____weekend passesthey sold_____ day passes

Answer 1

By setting up a system of equations and solving for the number of weekend passes (x) and day passes (y), it was determined that 2,236 weekend passes and 2,437 day passes were sold.

Step-by-step explanation:

To solve this problem, we can set up a system of equations using the given information. Let's define x as the number of weekend passes sold and y as the number of day passes sold. According to the problem, day passes were sold for $105 each and weekend passes for $111 each, making the total sales amount to $504,081. We also know that 201 more day passes than weekend passes were sold. So, we can create the following equations:

• 105y + 111x = 504,081 (Total sales equation)
• y = x + 201 (Day passes sold equation)

Now we can substitute the expression for y from the second equation into the first equation:

• 105(x + 201) + 111x = 504,081

Expand and simplify:

• 105x + 21,105 + 111x = 504,081
• 216x + 21,105 = 504,081
• 216x = 504,081 - 21,105
• 216x = 482,976
• x = 482,976 / 216
• x = 2,236 (weekend passes sold)

Substitute value of x into the second equation to get y:

• y = 2,236 + 201
• y = 2,437 (day passes sold)

Thus, they sold 2,236 weekend passes and 2,437 day passes.

Answer 2

We have to unknown values to find the number of day passes, we call x, and the number of weekend passes, we call y.

So we hhave two unknown variables we need two equations.

From the question we know the price of each ticket and the total sales, and also we know that they sold 201 more day passes than weekend passes.

In equation this is:

`\begin{gathered} \text{Number of tickets:} \\ x=y+201 \\ \text{Total sales:} \\ 105\cdot x+111\cdot y=504,081 \end{gathered}`

From the equations above, we can replace the x=y+201 into the second equation:

`\begin{gathered} x=y+201 \\ 105\cdot(y+201)+111\cdot y=504081 \\ 105y+111y+105\cdot201=504081 \\ (105+111)y=504081-105\cdot201=504081-21105 \\ 216y=482976 \\ y=(482976)/(216)=2236 \\ x=y+201=2236+201=2437 \end{gathered}`

They sold 2437 day passes and 2236 weekend passes