What equation should I write to find the answer?

Question

I was thinking about 3s - 40 = 680 but I'm not sure. Here's the problem:The members of the Drama Club sold a total of 680 adult and student tickets to their spring play. The number of adult tickets they sold was 40 less than triple the number of student tickets sold. Write a system of linear equations and use it to find out how many of each type of ticket the Drama CLub sold.

Answer 1

So, Angela, you need a system of equations. With two variables, that's usually two equations.

 

If they sold 680 total tickets, subtracting 40 from 3s means your total is more than 680.

 

What are our two variables. Let's let a = the number of adult and s = the number of student tickets sold.

 

If they sold 680 tickets, a + s = 680.

 

What was 40 less than three times the number of student tickets? Adult tickets! a = 3s - 40

 

a + s = 680

a = 3s - 40

 

We can solve this in a few different ways, but here's what jumps out at me.

 

Either way, solve the first equation for a.

 

a = 680 - s

 

Now, a equals two different things, which means they are equal to each other.

 

3s - 40 = 680 - s

 

Solve this for s, then plug your answer into the first equation and solve for a.