A movie theater manager wants to know how many adults and how many children pay admission to a particular movie. The theater charges $10.00 for adult tickets and $5.00 for child tickets. At a showing where 210 tickets were sold the theater collected $1,355.00. Write a system of equations and determine the number of adult tickets sold and the number of child tickets sold.
Could you please show the work on how to do this?
A movie theater manager wants to know how many adults and how many children pay admission to a particular movie. The theater charges $10.00 for adult tickets and $5.00 for child tickets. At a showing where 210 tickets were sold the theater collected $1,355.00. Write a system of equations and determine the number of adult tickets sold and the number of child tickets sold.
Could you please show the work on how to do this?
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To solve this problem, we need to set up a system of equations based on the given information.
Let's assume that the number of adult tickets sold is represented by 'a', and the number of child tickets sold is represented by 'c'.
Based on the information given, we can create two equations:
Equation 1: Total number of tickets sold: a + c = 210
Equation 2: Total amount collected: 10a + 5c = 1355
Now, we have a system of equations to solve. There are different methods to solve the system, but in this case, we will use the substitution method:
Step 1: Solve Equation 1 for 'a' in terms of 'c':
a = 210 - c
Step 2: Substitute the value of 'a' from Step 1 into Equation 2:
10(210 - c) + 5c = 1355
Step 3: Distribute 10 into the parentheses:
2100 - 10c + 5c = 1355
Step 4: Combine like terms:
-5c = 1355 - 2100
-5c = -745
Step 5: Divide both sides of the equation by -5 to solve for 'c':
c = -745 / -5
c = 149
Step 6: Substitute the value of 'c' into Equation 1 to solve for 'a':
a + 149 = 210
a = 210 - 149
a = 61
Therefore, the number of adult tickets sold is 61, and the number of child tickets sold is 149.
Let
A = the number of adult tickets
C = the number of children tickets
Then,
A + C = 210 and
10A + 5C = 1355
Can you take it from here?