There are 155 people at the basketball game. Tickets for the game are $2.50 for students and $4 for adults. If the total ticket money received is $492.50 how many students and adults attended the game?
A = 155 - S
$2.50S + $4.00A = $492.50
Substitute 115-S for A in the second equation and solve for S. Insert that value into the first equation to solve for A. Check by putting both values into the second equation.
To find out how many students and adults attended the game, we can use a system of equations.
Let's assume that the number of students at the game is 's' and the number of adults is 'a.'
According to the problem, we know that there are 155 people in total, so we can write the first equation as:
s + a = 155 (Equation 1)
We also know that the total ticket money received is $492.50, which we can express as the sum of the money from students and adults:
2.50s + 4a = 492.50 (Equation 2)
Now we have a system of equations (Equation 1 and Equation 2) that we can solve to find the values of 's' and 'a'.
To solve the system, we can use either substitution or elimination method. Let's use elimination method:
Multiply Equation 1 by -2.50 to cancel out 's' when we add the equations:
-2.50s - 2.50a = -387.50 (Equation 3)
2.50s + 4a = 492.50 (Equation 2)
Adding Equation 3 and Equation 2, we get:
-2.50a + 4a = 492.50 - 387.50
1.50a = 105
a = 105 / 1.50
a = 70
Now we know that there were 70 adults at the game.
Substitute the value of 'a' back into Equation 1 to find 's':
s + 70 = 155
s = 155 - 70
s = 85
Therefore, there were 85 students at the game.
So, there were 85 students and 70 adults in total who attended the game.