The laurelwood pta is presenting it's 5th annual talent show and Kate is collected tickets at the door the gym is filled with 215 students and adults. Students tickets are .50 and adults tickets are 2.00. If Kate collected 250.00. How many adults and how many students purchased tickets?
A=125
c is 80
To determine the number of adults and students who purchased tickets, we can use algebraic equations. Let's assume "a" represents the number of adult tickets sold and "s" represents the number of student tickets sold.
We are given the following information:
1. The gym is filled with 215 students and adults, so the total number of tickets sold is equal to 215.
Equation 1: a + s = 215
2. The total amount collected is $250.00. The cost of each adult ticket is $2.00, and the cost of each student ticket is $0.50.
Equation 2: 2a + 0.5s = 250
Now, we can solve this system of equations to find the values of "a" and "s".
First, let's multiply Equation 1 by 2 to eliminate the decimals:
2(a + s) = 2(215)
2a + 2s = 430
Now we have the system of equations:
2a + 0.5s = 250 (Equation 2)
2a + 2s = 430 (Result of multiplying Equation 1 by 2)
Subtracting Equation 2 from the modified Equation 1 eliminates "a":
(2a + 0.5s) - (2a + 2s) = 250 - 430
0.5s - 2s = -180
-1.5s = -180
To isolate "s", we divide both sides of the equation by -1.5:
s = -180 รท -1.5
s = 120
Now, substitute the value of "s" into Equation 1 to find "a":
a + 120 = 215
a = 215 - 120
a = 95
Therefore, 95 adults and 120 students purchased tickets for the talent show at Laurelwood PTA's 5th annual talent show.
a + c = 215
2a + .5c = 250
Now just solve for a and c.