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
Leni [432]
3 years ago
14

A movie theater has a seating capacity of 235. The theater charges $5 for children, $7 for students, and $12 for adults. There a

re half as many adults as there are children. If the total ticket sales was $1706, How many children, students, and adults attended?
Mathematics
1 answer:
Annette [7]3 years ago
7 0

Answer:

61 adults, 122 children, and 52 students

Step-by-step explanation:

Let a = amount of adults, c = amount of children, and s = amount of students.

Let's go over what we know:

total amount: 235

twice as many children as adults

children: $5

student: $7

adult: $12

Using this information, we can determine the following:

a = 1/2c

235 = c + s + a

1706 = 5c + 7s + 12a

Since we know a = 1/2c, plug 1/2c in for a. The equations become:

235 = c + s + 1/2c

1706 = 5c + 7s + 6c

Now, solve the inequalities by substitution.

235 = c + s + 1/2c

235 = 1 1/2c + s

-s + 235 = 1 1/2c

-s = -235 + 1 1/2c

s = 235 - 1 1/2c

Now, plug in the value for s into the other equation.

1706 = 5c + 7(235 - 1 1/2c) + 6c

-5c + 1706 =  7(235 - 1 1/2c) + 6c

-5c = -1706 + 7(235 - 1 1/2c) + 6c

-5c = -1706 + 1645 - 21c/2 + 6c

-5c = -61 - 21c/2 + 6c

-5c = -61 - 9c/2

c = 122

Now, plug in the value for c into the value of s.

s = 235 - 1 1/2(122)

s = 235 - 183

s = 52

Finally, plug in the value for c into the value of a.

a = 1/2(122)

a = 61

To check, add up all values to make sure they equal 235.

61 + 52 + 122 = 235.

Therefore, the final answers are 61 adults, 122 children, and 52 students.

You might be interested in
If (x+2) is a factor of x^3-6x^2+kx+10, k=
Alja [10]
If a binomial (x-a) is a factor of a polynomial, then a is a root of this polynomial.

(x+2)=(x-(-2)) \Rightarrow a=-2\\\\
(-2)^3-6\cdot(-2)^2+k\cdot(-2)+10=0\\
-8-24-2k+10=0\\
-2k=22\\\
\boxed{k=-11}


3 0
2 years ago
Helppppppp mmeeeeee plllzzzzz
nikdorinn [45]

Answer: the answer is 6

Step-by-step explanation:

7 0
3 years ago
Trini rode her bike 12 miles on Friday. She rode 14 miles on Saturday and 15 miles on Sunday. How many miles did she ride in all
loris [4]

Answer: 41

Step-by-step explanation:

12+14+15= 41

4 0
1 year ago
Which of the following represents the expression 3 3 3 3 5 5 5 5 5 5
Mice21 [21]

Answer:

Msjusjsudjdudududusuhdu

6 0
2 years ago
A study was conducted on 64 female college athletes. The researcher collected data on a number of variables including percent bo
Leni [432]

Answer:

Hello please your question is in-complete attached is the complete question

degree of freedom = -62.90 ( e )

Step-by-step explanation:

The formula for calculating the F-statistic/test statistic is

test - statistic  = Coef ( LBW) / SE Coef ( LBW )

                       = -0.72399 / 0.01151

                       = - 62.90

the degree of freedom the F-statistic has = -62.90

F-statistic test is any statistical test in which the test statistic has an F-distribution under the null hypothesis. the value of the test can be gotten from running an ANOVA test or regression analysis on the statistical models

4 0
2 years ago
Other questions:
  • Please hurry i need this done now 15 points and brainliest
    14·2 answers
  • What is 275,608 rounded to the nearest thousand
    13·1 answer
  • 20. Which problems will have two decimal places in the product?Mark all that apply.531 x 107.4 x 10(A) 5 X 0.89E 3.2 x 43(D) 6.1
    11·1 answer
  • 99 points help SHOW YOUR WORK Q+B=13. When B+3=0
    5·2 answers
  • Taxi Fares are normally distributed with a mean fare of $22.27 and a standard deviation of $2.20.
    8·1 answer
  • .solve for c <br> c−1.5+6.8=0.6<br><br> I NEED HELP
    7·1 answer
  • How many subsets does set A have if set A has 3 elements
    11·1 answer
  • Pls Some Help me Asap Hot ta Get this done in 1st per
    8·1 answer
  • Lydia feeds her dog everyday from the same bag of dog food. She opened a new bag that contains 52 cups of food. if her dog eats
    15·1 answer
  • PLEASE HELPP i’ll mark u brainliest
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!