Question

Adult tickets for the school musical sold for 3.50 and student tickets sold for 2.50. three hundred twenty one tickets were sold altogether for 937.50. how many of each kind of ticket were sold?

Answer 1

A total of 135 adult tickets and 186 student tickets were sold for the school musical. We arrived at this by setting up a system of linear equations and solving for the number of each type of ticket sold.

Step-by-step explanation:

To solve the problem of the number of adult and student tickets sold for the school musical, we can set up a system of equations. Let's define A as the number of adult tickets and S as the number of student tickets. We are given the following two equations based on the information provided:

1. 3.50A + 2.50S = 937.50 (This equation represents the total amount of money made from ticket sales.)
2. A + S = 321 (This equation represents the total number of tickets sold.)

We can multiply the second equation by 2.50 to help eliminate S when we subtract the equations:

1. 2.50A + 2.50S = 802.50 Now, we subtract this new equation from the first equation:

3.50A + 2.50S - (2.50A + 2.50S) = 937.50 - 802.50

This simplifies to:

1.00A = 135

Dividing both sides by 1.00, we find:

A = 135

With the number of adult tickets known, we can substitute back into the second equation to find the number of student tickets:

135 + S = 321

S = 321 - 135

S = 186

Therefore, 135 adult tickets and 186 student tickets were sold.

Answer 2

Let a represent adult tickets
Let s represent student tickets


3.50 a + 2.50 s = $937.50 eqation 1


three hundred twenty one tickets were sold altogether

a + s = 321 equation 2
s= 321 - a

we replace it in equation 1 so

3.50a + 2.50s = 937.50
3.50a + 2.50(321-a)=937.50
3.50a+802.5-2.50a=937.50
3.50a-2.50a+802.5=937.50
1.00a+802.5=937.50

a=135

and s=321-135= =186