there are a 1000 tickets. Price for children's ticket is 6.5. Adult tickets are 9.5. total tickets sales are 8444. how many adult and children tickets are sold. Using binomials to solve.
x+y = 16 (1 child + 1 Adult = 16)
6.5X + 9.5Y = 8444
6.5(16-y) + 9.5Y = 8444
What am I doing wrong?
do not mix up the quantity with the prices. We know there are 1000 tickets, so
x+y = 1000
now add up the prices, remembering that x and y are the number of tickets:
6.5x + 9.5y = 8444
you used x,y for prices in one place, number of tickets in the other. Using the two equations I showed above,
6.5x + 9.5(1000-x) = 8444
3x = 1056
x = 352
so, y = 1000-x = 648
It seems like you are attempting to solve the problem using a system of equations. However, there seems to be a mistake in one of your equations.
To correctly set up the system of equations, let's define the variables:
Let x represent the number of children's tickets sold.
Let y represent the number of adult tickets sold.
Now, let's set up the equations based on the given information:
1. The total number of tickets sold is 1000, so the first equation is x + y = 1000.
2. The total ticket sales amount to 8444. Since the price of a children's ticket is $6.5 and the price of an adult ticket is $9.5, we can set up the second equation: 6.5x + 9.5y = 8444.
Now, let's take a closer look at your attempt to solve the system using binomials.
You wrote: 6.5(16 - y) + 9.5y = 8444
The error in your equation is that the coefficient of 16 should not be 6.5. In the first equation x + y = 16, the coefficient of x and y is 1 because there are no multiplied variables. Therefore, the correct equation should be:
6.5x + 9.5y = 8444
To solve this system of equations, you can use various methods, such as substitution or elimination. With the given equations x + y = 1000 and 6.5x + 9.5y = 8444, you can substitute the value of x from the first equation into the second equation to solve for y. Once you have the value of y, you can substitute it back into the first equation to find the value of x.