Jarrett was selling tickets at local carnical. The tickets cost 2.00 for adults and 1.50 for children. How many of each kind of ticket did he sell if he sold a total of 300 tickets for $525?
K+A=300
1.5K+2A=525
multiply the first equation by 2, then subtract the second equation, and you get...
.5K=600-525
K=150 tickets
A=150 tickets
To solve this problem, we can use a system of equations. Let's assign variables to the unknowns:
Let's assume the number of adult tickets sold is 'x', and the number of children tickets sold is 'y'.
According to the given information, the cost of an adult ticket is $2.00 and the cost of a child ticket is $1.50.
Therefore, we can create two equations based on the total number of tickets sold and the total amount of money collected:
Equation 1: x + y = 300 (equation based on the total number of tickets sold)
Equation 2: 2x + 1.5y = 525 (equation based on the total amount of money collected)
Now, we can solve this system of equations to find the values of 'x' and 'y'.
Using the substitution method, we can solve Equation 1 for x:
x = 300 - y
Now, substitute this expression for x in Equation 2:
2(300 - y) + 1.5y = 525
Simplify the equation:
600 - 2y + 1.5y = 525
600 - 0.5y = 525
Rearrange the equation to isolate y:
-0.5y = 525 - 600
-0.5y = -75
Divide both sides by -0.5 to solve for y:
y = (-75) / (-0.5)
y = 150
Now that we have the value of y (150), we can substitute it back into Equation 1 to find the value of x:
x + 150 = 300
x = 300 - 150
x = 150
Therefore, Jarrett sold 150 adult tickets and 150 children tickets.