1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Korvikt [17]
3 years ago
12

A movie theater has a seating capacity of 337. 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 $ 2456, How many children, students, and adults attended?
children attended.
students attended.
adults attended.
Mathematics
1 answer:
valentinak56 [21]3 years ago
4 0

Answer: 194 children, 46 students and 97 adults attended.

Step-by-step explanation:

Let x represent the number children that attended.

Let y represent the number students that attended.

Let z represent the number adults that attended.

The movie theater has a seating capacity of 337. Assuming it was filled to capacity, It means that

x + y + z = 337- - - - - - - - - - -1

The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. If the total ticket sales was $ 2456, it means that

5x + 7y + 12z = 2456- - - - - - - - -2

There are half as many adults as there are children. It means that

z = x/2

x = 2z

Substituting x = 2z into equation 1 and equation 2, it becomes

2z + y + z - 337

y + 3z = 337- - -- - - - - - -3

5 × 2z + 7y + 12z = 2456

10z + 7y + 12z = 2456

7y + 22z = 2456- - - - - - - -4

Multiplying equation 3 by 7 and equation 4 by 1, it becomes

7y + 21z = 2359

7y + 22z = 2456

Subtracting, it becomes

- z = - 97

z = 97

x = 2z = 2 × 97

x = 194

Substituting x = 194 and z = 97 into equation 1, it becomes

194 + y + 97 = 337

y + 291 = 337

y = 337 - 291

y = 46

You might be interested in
Ralph is purchasing a new gaming system for $300.00. He is trying to decide whether he wants to use cash or his credit card to p
ra1l [238]

Using cash can help Ralph improve his credit score is just untrue in so many ways.


The answer is choice A because the statement does not justify Ralph's use of cash.

6 0
3 years ago
Read 2 more answers
Please help me !<br> Which one is it?<br> (9Ft IS WRONG)
9966 [12]
Here’s the correct answer and the way i got to it. Hope this helps :)

4 0
2 years ago
How many solutions can be found for the equation 3x − 2 = 3x + 5?
aksik [14]

Answer:

Zero

Step-by-step explanation:

there is no solution the sides are uneven. if you solve for it 3x and 3x cancels out each other leaving you with -2=5

7 0
3 years ago
Read 2 more answers
- Write a recursive formula to represent the sequence below.<br> (3,7, 11, 15, 19,23,27,31,35, ...)
NemiM [27]

<em><u>The recursive formula to find nth term of sequence is:</u></em>

a_n = 4n - 1 \text{ where } n \geq 1 and n  = 1, 2, 3, ....

<em><u>Solution:</u></em>

Given a sequence is:

3, 7, 11, 15, 19, 23, 27, 31, 35

<em><u>Let us find the difference between terms</u></em>

7 - 3 = 4

11 - 7 = 4

15 - 11 = 4

19 - 15 = 4

23 - 19 = 4

27 - 23 = 4

31 - 27 = 4

35 - 31 = 4

Thus the difference between terms is constant

Thus the given sequence is arithmetic sequence

An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant

<em><u>The nth term of arithmetic sequence is given by:</u></em>

a_n =a_1+(n-1)d

a_n = the nᵗʰ term in the sequence

a_1 = the first term in the sequence

d = the common difference between terms

Here in the given sequence

d = 4

a_1=3

Substitute in above formula,

a_n = 3 + (n-1)(4)\\\\a_n = 3 + 4n - 4\\\\a_n = 4n - 1

<em><u>Thus the recursive formula to find nth term of sequence is:</u></em>

a_n = 4n - 1 \text{ where } n \geq 1 and n = 1, 2, 3, ......

8 0
2 years ago
Simplify completely quantity x squared minus 3 x minus 54 over quantity x squared minus 18 x plus 81 times quantity x squared pl
oee [108]
Your statemtent is incomplete.

I found the samestatment with the complete words: <span>Simplify completely quantity x squared minus 3 x minus 54 over quantity x squared minus 18 x plus 81 times quantity x squared plus 12 x plus </span>36 over x plus 6

Given that your goal is to learn an be able to solve any similar problem, I can teach you assuming that what I found is exactly what you need.

x^2 - 3x - 54            x^2 + 12x + 36
------------------    x   ---------------------
x^2 - 18x + 81              x + 6

factor x^2 - 3x - 54 => (x - 9)(x + 6)

factor x^2 - 18x + 81 => (x - 9)^2

factor x^2 + 12x + 36 = (x + 6)^2

Now replace the polynomials with the factors=>

(x - 9) (x + 6) (x + 6)^2        (x + 6)^2       x^2 + 12x + 36
------------------------------ =  --------------- = --------------------
    (x - 9)^2 (x + 6)                 (x - 9)               x - 9

4 0
3 years ago
Read 2 more answers
Other questions:
  • Brainliest: Please, I need help on this one!!
    11·1 answer
  • Please help with these 2 !! Thank you
    6·1 answer
  • Leslie babysat the Thompson twins for 110 hours during the summer. This was 5 1/2 times as many hours as Tom babysat the twins.
    14·1 answer
  • The equation for m=0,(-7,8)
    12·1 answer
  • Translate this sentence into an equation.
    8·1 answer
  • A(7-1), B(6, 4) and C(5, 5) are three
    11·1 answer
  • H/6-1=-3 solve for H
    7·1 answer
  • How do you solve this? Need help please
    14·1 answer
  • Which of the following is the algebraic representation for a translation 7 units left and 6 units up?
    6·1 answer
  • Evaluate the expression 5+3​
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!