Suppose 200 tickets were sold for a particular concert. Some tickets cost $10 each, and others cost $5 each. If total ticket sales were $1,750, how many of the more expensive tickets were sold.

To solve this, we will need to set up a system of equations. There are 2 units here: Tickets and money. We will need one equation for each unit. Let the more expensive ticket be x, and the less expensive ticket be y.

For tickets, we know that there were 200 total sold. That means that the total amount of tickets sold, x and y, is equal to 200. In equation form:

200 = x + y

For money, we know that total ticket sales were 1750 dollars. We also know that some tickets cost 10 dollars, while others cost 5 dollars. The sum of the products of each ticket cost and the amount of tickets sold will be equal to the total ticket sales. In equation form:

1750 = 10x + 5y

Now we have the system:

200 = x + y

1750 = 10x + 5y

To solve this system by substitution, isolate one of the variables in the first equation. I'll isolate x.

200 = x + y

200 - y = x

x = 200 - y

Substitute this expression (200 - y) for x into the second equation and solve for y.

1750 = 10x + 5y

1750 = 10 (200 - y) + 5y

1750 = 2000 - 10y + 5y

1750 = 2000 - 5y

-250 = - 5y

50 = y

Substitute 50 for y into either of the original equations to find x.

200 = x + y

200 = x + 50

150 = x

Lastly, substitute the x - and y-values into each original equation to check work.

200 = x + y - -> 200 = 150 + 50 - -> 200 = 200 - -> True

1750 = 10x + 5y - -> 1750 = 10 (150) + 5 (50) - -> 1750 = 1500 + 250 - -> 1750 = 1750 - -> True

Answer:

150 of the more expensive tickets were sold.

Let the 5 dollar tickets sold be x and the 10 dollar tickets be y. We can then create a system of equations to solve for the amounts.

This equation is the total amount of tickets sold.

x+y=200

This equation deals with the total amount of money made.

5x+10y=1750

Lets multiply the first equation by 5 on both sides.

5 (x+y) = 5 (200)

5x+5y=1000

Now we use the elimination method by subtracting one equation from the other.

5x+10y=1750

- (5x+5y=1000)

0+5y=750

Next, we can solve for y in this equation.

5y=750

y=150

So, 150 of the more expensive ticket was sold. Finally, we can plug in y into one of the equations and solve for x.

x+150=200

x=50

Thus, 50 of the less expensive tickets were sold.