Word problem

Question

The Concordia theatre contains 500 seats and the ticket prices for a recent play were  $43 for adults and  $28 for children. For one sold out matinee if the total proceeds were  $16,805 how many of each type of ticket were sold? 

 

Can you break down each step of how you come up with your answer 

Answer 1

Let's set this up as a linear equations problem. Let's call the number of adult tickets sold x, and the number of children tickets sold y.

 

If there were 500 seats and the theatre was sold out, then x and y must add to 500. So we have one equation: x + y = 500.

 

Next, if the total proceeds were 16,805 then 43 times x and 28 times y must add to 16,805. So we have another equation: 43x + 28y = 16805.

 

Now we have two equations and two variables, which is what we need to solve a linear equations problem.

 

Let's use the simpler equation and solve for y.

 

x + y = 500 (subtract x from each side)

y = 500 - x

Now we will use this value of y and plug it into the other equation.

 

43x + 28(500 - x) = 16805 (expand the polynomial)

43x + 14000 - 28x = 16805 (collect like terms)
15x + 14000 = 16805 (subtract 14000 from each side)

15x = 2805 (divide each side by 15)

x = 187

 

So now we know that there were 187 adult tickets sold. And we can plug this value in for x now in the second, simpler equation.

 

187 + y = 500 (subtract 187 from each side)

y = 313

 

So there were 313 children sold and 187 adult tickets sold.