Question

Tickets to a concert cost either $12 or $15. A total of 300 tickets are sold, and the total receipts were $4,140. How many of each kind of ticket were sold? First complete the equations below, where x stands for $12 tickets and y stands for $15 tickets. 12x+15y=4,140;x+y=[?]

Answer 1

Using the system of equations x + y = 300 and 12x + 15y = 4,140, we find that 120 tickets were sold at $12 each, and 180 tickets were sold at $15 each.

Step-by-step explanation:

To determine how many of each kind of ticket were sold when tickets to a concert cost either $12 or $15, we can set up a system of linear equations based on the given information. Let x represent the number of $12 tickets and y represent the number of $15 tickets. The total number of tickets sold is 300, so we have:

x + y = 300

The total amount of money from ticket sales is $4,140, so we also have the equation:

12x + 15y = 4,140

To find the values of x and y, we can use the method of substitution or elimination. For example, using the substitution method, we can express y in terms of x using the first equation:

y = 300 - x

Substitute this expression for y into the second equation:

12x + 15(300 - x) = 4,140

Now we solve for x:

12x + 4,500 - 15x = 4,140

-3x + 4,500 = 4,140

-3x = -360

x = 120

Now that we have x, we can solve for y:

y = 300 - 120 = 180

Therefore, 120 tickets were sold at $12 each and 180 tickets were sold at $15 each.