Math, asked by annyeonghaseyo02, 1 month ago

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

Answered by mathdude500
6

\large\underline{\sf{Solution-}}

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

\rm \implies\:\boxed{ \tt{ \: 8x + 2y + 3z = 2340 \: }} -  -  - (1)

According to second condition

↝ The theater sold 600 tickets.

\rm \implies\:\boxed{ \tt{ \: x + y + z = 600 \: }} -  -  - (2)

According to third condition

↝ The children's ticket sold twice the that of adult tickets.

\rm \implies\:\boxed{ \tt{ \: y = 2x \: }} -  -  -  - (3)

On substituting the value of y in equation (1), we get

\rm :\longmapsto\:8x + 2(2x) + 3z = 2340

\rm :\longmapsto\:8x + 4x + 3z = 2340

\rm :\longmapsto\:12x+ 3z = 2340

\rm :\longmapsto\:3(4x+ z) = 2340

\bf\implies \:4x + z = 780 -  -  - (4)

Now, again on substituting the value of y in equation (2), we get

\rm :\longmapsto\:x + 2x + z = 600

\bf\implies \:3x + z = 600 -  -  -  - (5)

On Subtracting equation (5) from equation (4), we get

\bf\implies \:x = 180 -  -  -  - (6)

On substituting value of x in equation (5), we get

\rm :\longmapsto\:3 \times 180 + z = 600

\rm :\longmapsto\:540 + z = 600

\rm :\longmapsto\:z = 600 - 540

\bf\implies \:z = 60 -  -  -  - (7)

On Substituting the value of x in equation (3), we get

\rm :\longmapsto\:y = 2 \times 180

\bf\implies \:y = 360 -  -  -  - (8)

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.

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