How Many $90 and $120 Tickets Were Sold at the Concert?

[Izekid]

To a music consert there were an Income of 85500$
There were 2 types of tickets sold, one that cost 90$ and one that cost 120$. Totaly there were 800 tickets sold, how many of each ticket was sold.

Here I Shall use the ordinary math equation M = pxX + pyY and solve the equation, and I have no idea how to solve it!?

Please Help me

 

[nocturnal]

To a music consert there were an Income of 85500$
There were 2 types of tickets sold, one that cost 90$ and one that cost 120$. Totaly there were 800 tickets sold, how many of each ticket was sold.

Here I Shall use the ordinary math equation M = pxX + pyY and solve the equation, and I have no idea how to solve it!?

You should help us out and let us know what the variables M, px, X, py, and Y stand for, for two reasons:
1) it makes it easier for us,
2) It shows us that you know how to interpret that equation.

You need as many equations as there are unknown variables. Here you have two unknown variables X and Y, the number sold of each type of ticket. You have only one equation so far so you need another one.

hint: what does X + Y equal?

 

[Architeuthis Dux]

!

I would like to clarify that this is not a question related to national economics. This is a basic math problem that can be solved using simple algebraic equations. The equation you have mentioned, M = pxX + pyY, is known as the general form of a linear equation, where M represents the total income, p represents the price of the tickets, X represents the number of tickets sold at price p, and Y represents the number of tickets sold at another price.

To solve this equation, we first need to create two equations using the given information.

Equation 1: 90X + 120Y = 85500 (Total income equation)
Equation 2: X + Y = 800 (Total number of tickets sold equation)

Next, we can use the substitution method or the elimination method to solve for the values of X and Y.

Substitution method:
- Solve Equation 2 for X: X = 800 - Y
- Substitute this value of X into Equation 1: 90(800 - Y) + 120Y = 85500
- Simplify the equation: 72000 - 90Y + 120Y = 85500
- Combine like terms: 30Y = 13500
- Solve for Y: Y = 450
- Substitute this value of Y into Equation 2 to find X: X = 800 - 450 = 350

Therefore, 350 tickets were sold at $90 each and 450 tickets were sold at $120 each.

Elimination method:
- Multiply Equation 2 by -90: -90X - 90Y = -72000
- Add this equation to Equation 1: -90X + 90X - 90Y + 120Y = -72000 + 85500
- Simplify the equation: 30Y = 13500
- Solve for Y: Y = 450
- Substitute this value of Y into Equation 2 to find X: X = 800 - 450 = 350

As you can see, both methods give the same result. Therefore, 350 tickets were sold at $90 each and 450 tickets were sold at $120 each. I hope this helps you to understand how to solve this problem. If you need further assistance, please reach out to a math tutor or your teacher for additional support.