How many adult tickets did they sell, how many student tickets did they sell ?

Question

The student drama club at a high school sold 200 tickets to Romeo and Juliet. There were two types of tickets: adult tickets for $10 each and the student tickets for $6 each. In total the club sold $1500 worth of tickets.

Answer 1

Let's start by identifying the variables and writing out two equations to make this easier.

A=Adult

S=Student

Eq#1: A+S= 200= Total tickets from both adults and students

Eq#2: 10A+6S= 1500= the price of adult tickets multiplied by the # of tickets sold and the price of student tickets multiplied by the number of tickets sold gives you the total cost of $1500.

Solve for either A or S in Eq#1. Here I will solve for A.

A= 200-S

Substitute the above into Eq#2:

10(200-S)+6S=1500

2000 - 10S+6S=1500

2000-4S=1500

-4S=-500

S=125 student ticktes

Substitute S in the equation to find A.

Eq#1: A+S= 200

A+125=200

A=75 Adult tickets

Now that we know how many of each ticket we have we can simply multiply.

75 adult tickets * $10= $750

125 student tickets *$6= 750

And just to check if our math is correct:

$750 +$750= $1500 which is as seen in the question stem

75 adult tickets + 125 student tickets= 200 tickets as seen in the question stem

Hope this helps!

Answer 2

We will need to use a system of equations to solve this! Let's say the # of adult tickets sold will be A and the # of child tickets sold will be C. We know when we add the # of adult and child's tickets sold, we get 200. So our first equation is:

A + C = 200

Now, each adult ticket is $10 and each child ticket is $6. When we add the revenue together we get a total profit of $1500. So our second equation is:

10A + 6C = 1500

Now we can solve using substitution. We solve one equation for a variable and plug it into the other equation:

A + C = 200------> A + C = 1200

10A + 6C = 1500 -C -C

A = 200 - C

10(200 - C) + 6C = 1500

2000 - 10C + 6C = 1500

2000 - 4C = 1500

-2000 -2000

-4C = -500

/ -4 / -4

C = 125 A + 125 = 200

-125 -125

A = 75

So 75 adult tickets were sold and 125 child's tickets were sold. Feel free to reach out if you have any additional questions! :)