Word problem

Question

For a concert there were 206 more tickets sold at the door that were sold in advance the tickets sold at the door cost $10 and the tickets sold in advance cost $6 the total amount of sales for both types of tickets was $6,828 how many of each type of ticket was sold

Answer 1

Here we go, Yee - a system of two equations in two unknowns.

 

x = tickets sold in advance

y = tickets sold at the door

 

Equation for tickets sold: y - x = 206

 

Equation for the cash proceeds from ticket sales:

6x + 10y = 6828

 

I am going to solve the equation for tickets sold for y:

y = x + 206

 

Then I am going to substitute this y solution into the equation for cash proceeds:

 

6x + 10(x + 206) = 6828

or 16x + 2060 = 6828

or 16x = 4768

 

so x = 298. And y = x + 206 = 504.

 

Sanity check: when you first start out with systems of equations, the teachers LOVE to give you problems with whole-number answers. And this is a problem that forces you to get whole-number answers, because you only buy whole tickets. So the two whole numbers you get in this answer are (to me) a very good sign. LOL