A movie theater has a seating capacity of 329. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2388, How many children, students, and adults attended?

___ children attended.
___students attended.
____adults attended.

Answers

Answer 1

Answer:

170 children

74 students

85 adults

Step-by-step explanation:

Given

Let:

[tex]C = Children; S = Students; A = Adults[/tex]

For the capacity, we have:

[tex]C + S + A = 329[/tex]

For the tickets sold, we have:

[tex]5C + 7S + 12A = 2388[/tex]

Half as many as adults are children implies that:

[tex]A = \frac{C}{2}[/tex]

Required

Solve for A, C and S

The equations to solve are:

[tex]C + S + A = 329[/tex] -- (1)

[tex]5C + 7S + 12A = 2388[/tex] -- (2)

[tex]A = \frac{C}{2}[/tex] -- (3)

Make C the subject in (3)

[tex]C = 2A[/tex]

Substitute [tex]C = 2A[/tex] in (1) and (2)

[tex]C + S + A = 329[/tex] -- (1)

[tex]2A + S + A = 329[/tex]

[tex]3A + S = 329[/tex]

Make S the subject

[tex]S = 329 - 3A[/tex]

[tex]5C + 7S + 12A = 2388[/tex] -- (2)

[tex]5*2A + 7S + 12A = 2388[/tex]

[tex]10A + 7S + 12A = 2388[/tex]

[tex]7S + 22A = 2388[/tex]

Substitute [tex]S = 329 - 3A[/tex]

[tex]7(329 - 3A) + 22A = 2388[/tex]

[tex]2303 - 21A + 22A = 2388[/tex]

[tex]2303 +A = 2388[/tex]

Solve for A

[tex]A = 2388 - 2303[/tex]

[tex]A = 85[/tex]

Recall that: [tex]C = 2A[/tex]

[tex]C = 2 * 85[/tex]

[tex]C = 170[/tex]

Recall that: [tex]S = 329 - 3A[/tex]

[tex]S = 329 - 3 * 85[/tex]

[tex]S = 329 - 255[/tex]

[tex]S = 74[/tex]

Hence, the result is:

[tex]C = 170[/tex]

[tex]S = 74[/tex]

[tex]A = 85[/tex]

Answer 2

Answer:

Down Below

Step-by-step explanation:

The answer is actually

162 children

86 students

81 adults

162x5=810

86x7=602

81x12=972

I found the original problem and the total ticket sale was $2384.

So I wrote the answers for the original problem just in case!

Ty for your time!


Related Questions

Which expression can be used to find the quotient of 184 and 8?
(184÷10)+(8÷2)
(160÷8)+(24÷8)
(18÷3)+(4-2)
(184÷4)+(8÷2)
????????

Answers

your answer is the second option, 160 divided by 8 plus 24 divided by 8.

Factor the expression completely.
35 + 2x2 – 24

Answers

Answer:

[tex]2x^{2} +11[/tex] cannot be simplified further

Step-by-step explanation:

Tina walked her dog 12 blocks. This is twice the number of blocks she walked yesterday. How far did Tina walk her dog yesterday?​

Answers

Answer: Hello, your Answer is Below ^^

Your Answer Is 6

Step-by-step explanation:

I Got the answer 6 Because 6 x 2 = 12

Tina Walked 12 blocks and Half of 12 Is 6

Hope this helps  you!

Have a great Day!

~Rainbow~

Answer:

the correct answer is 6

Step-by-step explanation:

since twice = 2 you'll need to do 12 divided by 2

which is equal to 6.

or you can simply just think what number is twice in 12.

The function f(x) is a quartic function and the zeros of f(x) are -4,-3,2 and 5. Assume the leading coefficient of f(x) is 1. Write the equation of the quartic polynomial in standard form

Answers

Answer:
f(x) = x⁴-6x³-13x²+66x+72
Step-by-step explanation:
Factors are: (x+3)(x+1)(x-4)(x-6)
[(x+3)(x+1)][(x-4)(x-6)]
[x²+3x+x+3][x²-4x-6x+24]
(x²+4x+3)(x²-10x+24)
x⁴+4x³+3x²-10x³-40x²-30x+24x²+96x+72
f(x) = x⁴-6x³-13x²+66x+72

The equation of the quartic polynomial in standard form is,

⇒ f (x) = x⁴ - 27x² - 14x + 120

What is Quadratic equation?

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;'

The function f(x) is a quartic function and the zeros of f(x) are -4,-3,2 and 5.

And, the leading coefficient of f(x) is 1.

Hence, We get;

The equation of the quartic polynomial in standard form is,

⇒ f (x) = 1 (x - (- 4)) (x - (- 3)) (x - 2) (x - 5)

⇒ f (x) = (x + 4) (x + 3) (x - 2) (x - 5)

⇒ f (x) = (x² + 7x + 12) (x² - 7x + 10)

⇒ f (x) = x⁴ - 7x³ + 10x² + 7x³ - 49x² + 70x + 12x² - 84x + 120

⇒ f (x) = x⁴ - 27x² - 14x + 120

Learn more about the quadratic equation visit:

brainly.com/question/1214333

#SPJ2

5) Abhasra invests $7,053 in a savings
account with a fixed annual interest rate of
3% compounded quarterly. What
will the account balance be after 4 years?

Answers

Answer:

After 4 years the account balance will be $ 7,948.67.

Step-by-step explanation:

Given that Abhasra invests $ 7,053 in a savings account with a fixed annual interest rate of 3% compounded quarterly, to determine what the account balance will be after 4 years, the following calculation must be performed:

7.053 x (1 + 0.03 / 4) ^ 4x4 = X

7,053 x 1.0075 ^ 16 = X

7.053 x 1.12699211 = X

7,948.67 = X

Therefore, after 4 years the account balance will be $ 7,948.67.

Question 7Partially correct answer. Your answer is partially correct. Try again.An article in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 273-279), considered arthroscopic meniscal repair with an absorbable screw. Results showed that for tears greater than 25 millimeters, 13 of 19 repairs were successful while for shorter tears, 22 of 30 repairs were successful.(a) Is there evidence that the success rate is greater for longer tears

Answers

This question is incomplete, the complete question is;

An article in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 273-279), considered arthroscopic meniscal repair with an absorbable screw. Results showed that for tears greater than 25 millimeters, 13 of 19 repairs were successful while for shorter tears, 22 of 30 repairs were successful.

a) Is there evidence that the success rate is greater for longer tears? Use alpha=0.05

Answer:

P-value = 0.6443

Now, since the p-value( 0.6443 ) is greater than the significance level (0.05), We fail to reject null hypothesis.

Therefore, there is no significant difference in the successive proportion ( rate ). [tex]p[/tex]₁ =  [tex]p[/tex]₂

Step-by-step explanation:

Given the data in the question;

         Sample of tears greater than 25;

number of successive repairs X₁ = 13

number of repair n₁ = 19

proportion of successive repairs [tex]p[/tex]₁ = 13/19 = 0.68

q₁ = 1 -  [tex]p[/tex]₁ = 1 - 0.68 = 0.32

        Sample of tears shorter than 25;

number of successive repairs X₂ = 22

number of repair n₂ = 30

proportion of successive repairs [tex]p[/tex]₂ = 22/30 = 0.73

q₂ = 1 -  [tex]p[/tex]₂ = 1 - 0.73 = 0.27

so;

H₀ : There is no significant difference in the successive proportions;  [tex]p[/tex]₁ =  [tex]p[/tex]₂

Hₐ : The successive rate is greater for longer tears [tex]p[/tex]₁ >

Significance level ∝ = 0.05

Test Statistics

Z =  ([tex]p[/tex]₁ -

so we substitute

Z =  ( 0.68 - 0.73 / √[ (0.68 ×0.32 / 19) + ( 0.73×0.27 / 30 ) ]

Z = -0.05 / √[ 0.01802 ]

Z = -0.05 / 0.1342

Z = -0.37  

P-value for the given test, p = P( Z > -0.37 )

= 1 - P( Z ≤ - 0.37 )

= 1 - 0.35569

P-value = 0.6443

Now, since the p-value( 0.6443 ) is greater than the significance level (0.05), We fail to reject null hypothesis.

Therefore, there is no significant difference in the successive proportion ( rate ). [tex]p[/tex]₁ =  [tex]p[/tex]₂

what is the volume of this rectangular prism 5/4×5/3×5/2​

Answers

Answer:

the answer is one!

Step-by-step explanation:

Answer:

answer: 125/24 cm3

volume= 5/3*5/2*5/4 cm3

=125/24 cm3

Please help asap!!!!

Answers

Answer:

[tex] m\widehat {MP} =46\degree [/tex]

Step-by-step explanation:

By inscribed angle theorem:

[tex] m\angle MQP=\frac{1}{2} \times \widehat {MP} [/tex]

[tex] 23\degree =\frac{1}{2} \times m\widehat {MP} [/tex]

[tex] 23\degree \times 2= m\widehat {MP} [/tex]

[tex] m\widehat {MP} =46\degree [/tex]

In the formula, l = a + (n - 1)d make d as the subject. Find d when l = 10, a = 2, n = 5.

Answers

Given:-

I = a + (n - 1)d [Given formula]

To Find:-

Find d when I = 10, a = 2, n = 5

Solution:-

I = a + (n - 1)d [Given]

Putting the value of I = 10, a = 2, n = 5 we get,

10 = 2 + (5 - 1)d

10 = 2 + 4d

10 - 2 = 4d

8 = 4d

d = [tex] \frac{8}{4} [/tex]

d = 2

Value of d is 2. [Answer]

Mr. Robert offers students piano lessons. The cost is $25 per student plus a one-time registration fee of $50. How many lessons can a particular student take if they want to pay less than $175?
Write an inequality to represent the situation.

Define your variable in the space below.

Solve the inequality to determine how many lessons the student can take. Be sure to TYPE all your computations

Answers

Answer:

20

Step-by-step explanation:

cause

Dean made a triangular wall shelf.
The sides of the triangle measure
14 inches, 8 inches and 8 inches.
Is the shelf a right triangle?
Explain.

Answers

Answer:

The shelf is not a right triangle

Step-by-step explanation:

Given

[tex]Sides = 14, 8, 8[/tex]

Required

Determine if it is a right triangle

To do this, we make use of Pythagoras theorem which implies that; the square of the longest side = the sum of the square of the two other sides.

So, we have:

[tex]14^2 = 8^2 + 8^2[/tex]

Evaluate all squares

[tex]196 = 64 + 64[/tex]

[tex]196 = 128[/tex]

The above is not true because:

[tex]196 \ne 128[/tex]

Hence, the shelf is not a right triangle

What’s the missing side length? Round to the nearest tenth please :)))

Answers

Answer:

the answer is 4.6

Step-by-step explanation:

the explanation is shown in the following attachment below...

hope this helps...

Help please I need to complete this before 12

Answers

Answer:

Look at the answers bolded below

Step-by-step explanation:

To get the reference angle, just subtract 115° from 180°

180 - 115 = 65

So the reference angle is 65°

I'm not sure how many coterminal angles you need, but to get them you could just add or subtract 360°.

For example, a positive coterminal angle could be:

115 + 360 = 475°

a negative coterminal angle could be:

115 - 360  = -245°

Hope this helped :)

1. Which color combination is the
mode for the students' votes?
A Blue/Gold
B Green/Silver
C Blue/White
D Black/Gold

Answers

Is there more to the question? If not I say D

As part of a study of corporate employees, the director of human resources for PNC, Inc. wants to compare the distance traveled to work by employees at its office in downtown Cincinnati with the distance for those in downtown Pittsburgh. A sample of 40 Pittsburgh employees showed they travel a mean of 370 miles per month. A sample of 35 Cincinnati employees showed they travel a mean of 380 miles per month. Do the Cincinnati employees travel the same distance to work, on average, as the Pittsburgh employees

Answers

Answer:

Both groups of Employees do not  travel the same distance to work hence we will reject the Null hypothesis

Step-by-step explanation:

40 Pittsburgh employees mean travel time = 370 miles

35 Cincinnati employees mean travel time = 380 miles

Both groups of Employees do not  travel the same distance to work hence we will reject the Null hypothesis

H0 : μ1 = μ2

H1 : μ1 ≠ μ2

mean = total distance  / Number of employees

For Pittsburgh

370 = x / 40

x = 370 * 40 = 14,800 miles

For Cincinnati

380 = y / 35

y = 380 * 35 = 13,300 miles

Please help I don’t understand it
I need a reason for both

Answers

9514 1404 393

Answer:

  23) insufficient number of corresponding sides/angles

  24) insufficient number of corresponding sides/angles

Step-by-step explanation:

In general, you need at least 3 corresponding parts to show triangle congruence. At least one of those must be a side. The attachment shows the ways triangles can be declared congruent. (HL works for right triangles, because we know the right angles are congruent to each other.)

__

23) A side is shown congruent (KL ≅ GH), and we know the vertical angles at J are congruent. However, we need another angle before we can declare the ∆GHJ congruent to anything. (One more side doesn't do it, because the two sides would not be on either side of the angle at J.)

  Reason: insufficient data

__

24) A side is shown congruent (MP ≅ QS), and an angle is shown congruent (∠M ≅ ∠Q). As in the previous problem, we need at least one more angle, or we need to know that MN ≅ QR before we can declare the triangles congruent.

  Reason: insufficient data

Jose reads his book at an average rate of 2.5 pages every four minutes. If Jose continues to read at exactly the same rate what method could be used to determine how long it would take him to read 20 pages?

Answers

it would take him 32 minutes. You could use divisoin and multiplecation to figure it out

Simplify the following rational expression.
(HELP PLS?)

Answers

Answer:

Simplified expression: [tex]\frac{1}{y+8 }[/tex].

The value of y that makes the expression undefined is y=-8.

Step-by-step explanation:

[tex]\frac{2y^{3}}{2y^{4}+16y^{3}}[/tex]

= [tex]\frac{2y^{3}}{2y^{3}(y+8) }[/tex]

(cancel out 2y³)

=[tex]\frac{1}{y+8 }[/tex]

A rational expression is undefined when the denominator (bottom number) is  zero. So, if y equalled -8, the expression would ultimately equal [tex]\frac{1}{0}[/tex], which is undefined.

Question 8 of 10 What is the median of this data set? 14, 18, 31, 34, 44, 50 AL32.5 O B. 33 C. 31.5 D. 31​

Answers

Answer:

a

Step-by-step explanation:

4n -6 = 10n
Simplify.

Answers

-----------------------------------------------------------------------------------------------------------------

Answer: n = -1

-----------------------------------------------------------------------------------------------------------------

add 6 to both sides of the equation.

4n − 6 = 10n

4n − 6 + 6 = 10n + 6

-----------------------------------------------------------------------------------------------------------------

simplify.

(add the numbers)

4n − 6 + 6 = 10n + 6

4n = 10n + 6

4n = 10n + 6

-----------------------------------------------------------------------------------------------------------------

subtract 10n from both sides.

4n − 10n = 10n + 6 − 10n

-----------------------------------------------------------------------------------------------------------------

simplify. (again)

(combine like terms)                                          (combine like terms)

4n − 10n = 10n + 6 − 10n                                   −6n = 10n + 6 − 10n

−6n = 6

-----------------------------------------------------------------------------------------------------------------

divide both sides by the same term.

−6n/−6 = 6/-6

n = 6/−6n = 6/−6

-----------------------------------------------------------------------------------------------------------------

simplify. (again)

(cancel terms that are in both the numerator and denominator)

n = 6/−6

(divide the numbers)

n = 6/−6

n = 1

-----------------------------------------------------------------------------------------------------------------

Answer:

n= -1

Step-by-step explanation:

what value of x will make the faction equivent 3/5=x/36

Answers

Answer:

x = 21.6

Step-by-step explanation:

Solution by Cross Multiplication

For the equation

35=x36

The cross product is

3×36=5×x

Solving for x

x=3×365

and reducing

x=21.6

Solution by Proportion

Since the equation is an equality

If

36 ÷ 5 = 7.2

Then it is true that

x ÷ 3 = 7.2

Solving for x

x = 3 × 7.2

x = 21.6

Bailey makes a conjecture that the product of two odd integers is always an odd integer. Which choice is the best proof of her conjecture

Answers

Answer:

D.

Step-by-step explanation:

Let (2a+1) be an odd number, and let (2b+1) be another odd number. The product 2(2ab+a+b)+1 is a multiple of 2 plus 1, which is an odd number.

Find the area of the complex figure.

Answers

Answer:

1,863

Step-by-step explanation:

1,873 is the answer..

f(x) = 36x, find f(3/2)


36


72


216


64

Answers

Answer:

f(5) = 6(5-2) = 18

Step-by-step explanation:

hope this help ~~~~~~~~------~~~~~~~~

is X greater than less than or equal to 106 degrees​

Answers

Answer:

Less

Step-by-step explanation:

lesssssssssssssssssssssssss thannnnnnnnnnn

What is the area of this figure?

Answers

Answer:

m

Step-by-step explanation:

Sarah had a sheet of paper that was 3 inches long and 7 inches wide. What is the perimeter of the paper

Answers

Answer: 20

Step-by-step explanation:

(3+7)*2 = 20

Answer:

20 square inches

Step-by-step explanation:

KETO-SNACKS Tenlos a la mano para

Answers

Answer:

Here's 21 yummy keto snacks:

https://www.healthline.com/nutrition/best-keto-snacks

Hope u love em <3

Step-by-step explanation:

Which of the following shows the extraneous solution to the logarithmic equation log7 (3x ^ 3 + 7) - 100 + (x) = 27

Answers

Answer: X=-4

Step-by-step explanation:

Should be B on Edge.

Answer: X = -4

Step-by-step explanation:

ILL GIVE THE BRAINLIEST pls help me with this question EVERYTHING IS IN THE PICTURE PLS HELP DUE TODAY ​​IF YOU PUT A WRONG ANSWER ILL REPORT YOU FASTER THAN ASSIGMENT IS DUE ​​​

Answers

Answer:  the correct answer should be 160 but you said that didnt work so try 480

Step-by-step explanation:  

I just did base times Hight 8*10 which is 80*6=480

hoped this helps:))

Answer:

80

Step-by-step explanation:

V= Bh/3

Area of base= (L × W) ÷2

(8×6)÷2 = 24

Multiply by height

24×10=240

Divide by 3 (since its a pyramid therefore has 3 sides)

240/3=80

80 is your answer

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