The drama club sold 65 fewer adult tickets at $5 each than they did student tickets for $3 each. The total value of all the tickets was $675. How many adult and children tickets were sold?

adults ticket sold = 60

student tickets = 125

Step-by-step explanation:

So we need to make a system of equations. Lets say the variable a stands for adults tickets and the variable s stands for student tickets. Our first equation is going to be

s-a=65

that is because there are 65 more student tickets than adults.

the second equation is going to be

3s+5a=675

that is because the tickets will add up 675.

Now we have to make sure one of the variable cancels out when we add them together. So we have to multiply the first equation by 5.

5[s-a=65]

3s+5a=675

So then we end up with

5s-5a=325

3s-5a=675

We need to add them together and we end up with.

8s=1000

We need to divide by 8

s then equals 125.

So there are 125 students tickets.

We now plug 125 back into one of the equations. To make things easy lets to the first equation.

s-a=65

125-a=65

move the 125 over

-a=-60

multiply by a negative

a=60

So you have 60 adults tickets