Maven’s movie theater charges $8.00 for adults, $2.00 for children and $3.00 for senior citizens. One day, the theater sold 600 tickets and collected $2340 in receipts. The children's ticket sold twice the that of adult tickets. How many adults, children and senior citizens went to Maven’s theater on that particular day? (Hint: x = adults, y = children, z = senior citizens)
Answers
Let assume that
↝ Number of adults = x
↝ Number of children = y
↝ Number of senior citizens = z
According to first condition
Maven’s movie theater charges $8.00 for adults, $2.00 for children and $3.00 for senior citizens and collected $ 2340.
So,
Amount collected from ticket of adults = $ 8x
Amount collected from ticket of childrens = $ 2y
Amount collected from ticket of senior citizens = $ 3z
According to second condition
↝ The theater sold 600 tickets.
According to third condition
↝ The children's ticket sold twice the that of adult tickets.
On substituting the value of y in equation (1), we get
Now, again on substituting the value of y in equation (2), we get
On Subtracting equation (5) from equation (4), we get
On substituting value of x in equation (5), we get
On Substituting the value of x in equation (3), we get
Hence,
- Number of adults = x = 180
- Number of children = 360
- Number of senior citizens = 60
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Basic Concept Used :-
Writing Systems of Linear Equation from Word Problem.
1. Understand the problem.
- Understand all the words used in stating the problem.
- Understand what you are asked to find.
2. Translate the problem to an equation.
- Assign a variable (or variables) to represent the unknown.
- Clearly state what the variable represents.
3. Carry out the plan and solve the problem.