define the variable, write the equation, solve and label.
Central middle school sold 50 tickits for one night of the shcool play. Student tickets sold for $2 each and adult tickets sold for $3 each. They took in $135. How many of each type of ticket did they sell?
50= A+S
2s+3a= $135
s= -a+50
2(-a+50) + 3a= 135
Now solve for a then plug in what you get for a and solve for s
s=15, a=35
secret says that maybe wrong sorry secret out
To solve this problem, let's define the variables:
Let's say the number of student tickets sold is 's' and the number of adult tickets sold is 'a'.
Now, let's write the equation based on the given information:
The total income from student ticket sales can be calculated by multiplying the number of student tickets sold by the price of each student ticket, which is $2.
So, the income from student ticket sales is 2s.
Similarly, the total income from adult ticket sales can be calculated by multiplying the number of adult tickets sold by the price of each adult ticket, which is $3.
So, the income from adult ticket sales is 3a.
The total income from both types of tickets sold is given as $135.
Therefore, the equation representing the total income can be written as:
2s + 3a = 135
Now, let's solve this equation to find the values of 's' and 'a'.
There are multiple ways to solve this equation, but in this case, we can use a technique called substitution.
Let's solve for 's':
From the equation, we can isolate 's' by subtracting 3a from both sides:
2s = 135 - 3a
Now, let's solve for 's' by dividing both sides by 2:
s = (135 - 3a) / 2
Now that we have an expression for 's', we can substitute it back into the original equation:
2s + 3a = 135
Substituting the expression for 's':
2[(135 - 3a) / 2] + 3a = 135
Simplifying, we get:
135 - 3a + 3a = 135
The '3a' terms cancel out, leaving:
135 = 135
This equation is true for any value of 'a'. It means that there are infinite solutions to this problem.
To find a specific solution, we need more information, such as the total number of tickets sold or any other constraints given in the problem statement.