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I am Lyosha [343]

2 years ago

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A movie theater is filled to its capacity of 350. The theater charges $4.50 for children, $7.50 for students, and $12.50 for adu

lts. There are half as many adults as there are students. If the total ticket sales was $2415, how many children, students, and adults attended. Write your answer as an ordered triple in the form (# of children, # of students, # of adults). For example, (1,2,3).

2 answers:

Leno4ka [110]2 years ago

4 0

Answer:

<h2>(170;120;60).</h2>

Step-by-step explanation:

<h3>We know that:</h3>

Capacity of the theater: 350 people.

Adults is half the students.

Children's cost: $4.50

Student's cost: $7.50

Adults' cost: $12.50

Total Sales: $2415

We are gonna call <em>x </em>the children, <em>y </em>the students and <em>z </em>the adults:

So, the equation to express the capacity of the theater would be:

$x+y+z=350$

But, $z=\frac{y}{2}$ (adults are have students)

So, the expression would be: $x+y+\frac{y}{2} =350$

<h3>Solving <em>y's </em>and Isolating <em>x </em>: </h3>

$x+\frac{3y}{2} =350\\x=350-\frac{3y}{2}$

<h3>Now, we need a expression for costs. We have:</h3>

$4.50x+7.50y+12.50z=2415$

<h3>Replacing the <em>x </em>and <em>z </em>equation:</h3>

$4.50(350-\frac{3y}{2} )+7.50y+12.50\frac{y}{2}=2415$

<h3>Now, we solve for <em>y</em>:</h3>

$1575-6.75y+7.50y+6.25y=2415\\07y=2415-1575\\7y=840\\y=\frac{840}{7} =120$

<h3>But, we know that adults are half as many students, so:</h3>

$z=\frac{y}{2}=\frac{120}{2} =60$

<h3>Lastly,</h3>

$x+y+z=350\\x+120+60=350\\x=350-120-60\\x=170$

<em>Therefore, there are 170 children, 120 students and 60 adults. Expressing the results as an ordered triple would be (170;120;60)</em>

7nadin3 [17]2 years ago

3 0

Answer:

Step-by-step explanation:

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Step-by-step explanation:

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tatyana61 [14]

Answer:

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Step-by-step explanation:

Here we have;

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The t test formula is therefore;

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