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
vichka [17]
3 years ago
14

A movie theater has a seating capacity of 197. 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 $ 1416, How many children, students, and adults attended?
____ children attended
____students attended
____adults attended
Mathematics
1 answer:
yarga [219]3 years ago
5 0

Answer: 74 children attended

86 students attended

37 adults attended

Step-by-step explanation:

Let x represent the number of children that attended.

Let y represent the number of students that attended.

Let z represent the number of adults that attended.

The movie theater has a seating capacity of 197. It means that

x + y + z = 197- - - - - - - - - - - - -1

The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. If the total ticket sales was $ 1416, It means that

5x + 7y + 12z = 1416- - - - - - - - - - 2

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

It means that

z = x/2

x = 2z

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

2z + y + z = 197

y + 3z = 197- - - - - - - - - - - - -3

5 × 2z + 7y + 12z = 1416

10z + 7y + 12z = 1416

7y + 22z = 1416- - - - - - - - - - - 4

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

7y + 21z = 1379

7y + 22z = 1416

Subtracting, it becomes

- z = - 37

z = 37

x = 2z = 2 × 37

x = 74

Substituting x = 74 and z = 37 into equation 1, it becomes

74 + y + 37 = 197

y = 197 - 74 - 37

y = 86

You might be interested in
the student to teacher ratio is 15:3. if there are 90 teachers at the school, how many students are there
mixas84 [53]
15x+3x=90\\
18x=90\\
x=5\\\\
15x=15\cdot5=\boxed{75}
8 0
3 years ago
Read 2 more answers
Michael and Lindsey are saving money. Michael begins with $20 and saves $5 per week. Lindsey begins with no money, but saves $10
True [87]
Let
x----------> number of weeks
y----------> saved money

we now that

<span>Michael begins with $20 and saves $5 per week
so
y=20+5x------> equation 1

and
</span><span>Lindsey begins with no money, but saves $10 per week
</span><span>y=10x-------> equation 2

</span><span>the number of weeks it will take for Lindsey and Michael to save the same amount of money is when equation 1 is equals to equation 2
</span>
therefore
20+5x=10x------> 10x-5x=20------> 5x=20-----> x=20/5-----> x=4 weeks

the answer is 
4 weeks
3 0
2 years ago
Can someone plz help me?
Oksanka [162]

Answer:

c

Step-by-step explanation:

c

7 0
3 years ago
Consider the following food chain:
USPshnik [31]

Answer:

A

Step-by-step explanation:

the plant will increase because no grasshopper will be present to eat them without the grasshopper the mice cannot eat so the mice population will decrease....

6 0
2 years ago
Read 2 more answers
Equation A: y = −x + 5
ioda
I am thinking the 3rd one >> -x+5=6x-2

(: (:
6 0
3 years ago
Other questions:
  • PLZZZZZZZZZ HELP ME FOR 25 POINTS!!!!!!!!!!!!!!!!!!!!Solve and show your work for each question. (a) What is 0.36^__(over 3 and
    12·1 answer
  • lila draws a 145° angle.Then ahe divides it into three smaller angels.one of the smaller angles measures 65° ,and the other two
    6·1 answer
  • CRS-2 emulsion weighs 8.4lb/gal. I purchased 1.51Ton. How many gallons did I purchase?
    9·1 answer
  • The volume of a cube is found by using the formula Alta third power where else side length if the side length is 4X to the third
    5·1 answer
  • Soft drinks cost $1.89 and refills cost $0.25 each. With $3.80 to spend on the soft drink and refills, what is the maximum numbe
    6·1 answer
  • 10 пожалуйста решите
    15·1 answer
  • Which equation represents the following word problem?
    5·2 answers
  • Plz, answer this question plz!
    5·2 answers
  • For each 50 mm of coloured fabric Nick uses to make his curtains, he also uses 10 cm of white fabric. Express the amount of whit
    13·1 answer
  • In football, the path that a defender must run to tackle the ball carrier is called the path of pursuit. If the ball carrier run
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!