Question

Dave sold 60 general and reserved tickets for a concert. He sold general tickets for $10 each and reserved tickets for $15 each collecting a total of $725. Write a system of equations to determine the number of tickets he sold at each price and solve your system of equations?

Answer 1

Answer:

The system is of equations is:

$\left\{ \begin{array}{ll} 10g+15r=725 & \quad \\ g+r=60 & \quad \end{array} \right.$

Where g is the amount of general tickets and r is the amount of reserve tickets.

35 general tickets and 25 reserve tickets were sold.

Step-by-step explanation:

Let general tickets be represented by g and reserved tickets be represented by r.

Each general ticket sells for $10 each and reserved tickets $15 each. Dave collected a total of $725. Thus:

$10g+15r=725$

And a total of 60 tickets were sold. Hence:

$g+r=60$

Our system of equations is:

$\left\{ \begin{array}{ll} 10g+15r=725 & \quad \\ g+r=60 & \quad \end{array} \right.$

We can solve by substitution. First, divide both sides of the first equation by 5:

$2g+3r=145$

Next, we can subtract a variable (r in this case) from the second equation:

$g=60-r$

Substitute:

$2(60-r)+3r=145$

Distribute:

$120-2r+3r=145$

Simplify:

$120+r=145$

Subtract:

$r=25$

Using the previous equation:

$g=60-r$

Substitute and evaluate:

$g=60-(25)=35$

So, 35 general tickets and 25 reserve tickets were sold.