A local venue is selling tickets to a show. They are selling $10 and $15 tickets, each with different seating. If the venue sells 1,000 tickets and collects a total of $12,200 from sales, how many of each type of ticket did they sell? Please explain the work

Let $10 tickets be (x)

Let $15 tickets be (y)

Now we know they sold 1000 tickets

And they earned 12,200 from sales

So we can say

X+Y=1000

10x+15y=12,200

We can do substitution

So lets find Y first

Y=1000-x (basically x+y=1000 but solved for Y)

10x+ 15 ( 1000-x)= 12,200

You’d get

10x+15000-15x=12200

Combine and solve for x and you’ll get

x=560

So we know that x is 560

We can just use that to solve for Y

Since X is 560 tickets

And 1000 tickets soled

1000-560=440

440 ($15) tickets

560 ($10) tickets