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
vladimir2022 [97]
3 years ago
11

Columbia Theater Company reviewed their receipts from opening weekend. They sold 83 adult tickets and 42 child tickets on Friday

night, collecting a total of $874. On Saturday night, they collected $1151 from 102 adults and 67 children. If 48 adults and 26 children attended the matinee on Sunday, how much money did the theater collect from ticket sales?
Mathematics
1 answer:
slava [35]3 years ago
5 0

Answer:

If 48 adults and 26 children attended the matinee on Sunday, the theater raised $ 514 from ticket sales.

Step-by-step explanation:

A system of linear equations is a set of linear equations that have more than one unknown, which are related through the equations.

In this case, being:

  • A: adult ticket price
  • C: child ticket price.

The system of equations is:

\left \{ {{83*A+42*C=874} \atop {102*A+67*C=1151}} \right.

The substitution method consists of isolating one of the two unknowns in one equation to replace it in the other equation. In this case you isolate C from the first equation:

83*A + 42*C= 874

42*C= 874 - 83*A

C=\frac{874 - 83*A}{42}

Substituting this expression in the second equation:

102*A + 67*\frac{874 - 83*A}{42}= 1151

and solving:

102*A + \frac{67}{42} *(874 - 83*A)= 1151

Multiply through by 42

42*102*A + 42*\frac{67}{42} *(874 - 83*A)= 42*1151

4,284*A + 67*(874-83*A)= 48,342

4,284*A + 58,558 - 5,561*A= 48,342

4,284*A - 5,561*A= 48,342 - 58,558

-1,277*A= -10,216

A=\frac{-10,216}{-1,277}

A= 8

Knowing that: C=\frac{874 - 83*A}{42} then:

C=\frac{874 - 83*8}{42}

C=\frac{874 - 664}{42}

C=\frac{210}{42}

C= 5

The price of an adult ticket is $8 and a child is $5. If 48 adults and 26 children attended the matinee on Sunday, then:

$8*48 adults + $5* 26 childen= $514

<u><em> If 48 adults and 26 children attended the matinee on Sunday, the theater raised $ 514 from ticket sales.</em></u>

<u><em></em></u>

You might be interested in
What is 5.618 rounded to the nearest whole number?
Nataly [62]
5.618 rounded to the nearest hundredth is 5.62.
5 0
3 years ago
Read 2 more answers
Which expression represents the volume, in cubic units, of
Phoenix [80]

Answer:It's A. I just took the test on e2020

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
The weight of an object on a particular scale is 145.2 lbs. The measured weight may vary from the actual weight by at most 0.3 l
joja [24]

1. Know what you're looking for:

The range is the difference between the lowest and highest values.

Your weight is 145.2 and can vary from the actual weight by maximum 0.3 lbs less or maximum 0.3 lbs more.


2. Calculate your lowest and highest values :


Lowest : 145.2 - 0.3 = 144.9 lbs

Highest : 145.2 + 0.3 = 145.5 lbs


3. Calculate the range of actual weights of the object :


145.5 - 144.9 = 0.6 lbs


--> The answer is: <u>The range of actual weights of the object is 0.6 lbs.</u>


There you go! I really hope this helped, if there's anything just let me know! :)

4 0
3 years ago
A survey of the readers of three daily news papers; Nation, standard and Kenya times showed the following results. i) A total of
daser333 [38]
N(N ∩ S ∩ K) = 10
n(ξ) = 250
n(S ∪ K) = 15 - 10 = 5
n(N ∪ S) = 20 - 10 = 10
n(N ∪ K) = 30 - 10 = 20
n(S) = 50 - 10 - 5 - 10 = 25
n(K) = 55 - 20 - 5 - 10 = 20
n(N) = 100 - 10 - 20 - 10 = 60

n(N ∪ S ∪ K) = 10 + 5 + 10 + 20 + 25 + 20 + 60 = 150

Therefore, n(N ∪ S ∪ K)' = 250 - 150 = 100

Therefore, 100 million people do not read any of the three papers.
7 0
3 years ago
Which length is 10 6 times greater than a nanometer?
crimeas [40]
A nanometer (nm) is 10⁻⁹ m.

Therefore
10⁶ x 1 nm = 10⁶(10⁻⁹ m) = 10⁻³ m

By definition,
10⁻³ m = 1 mm (millimeter)

Answer: 1 millimeter
8 0
3 years ago
Other questions:
  • How many roots does the polynomial function, y=(x-8)(x+3)^2 have?
    11·2 answers
  • Here is a floor plan for a bedroom. Use this floor plan for the next several days
    13·1 answer
  • A user returned a tablet because of its battery life. Find the probability that it was returned after a year.
    6·1 answer
  • Select the value(s) that represent
    15·1 answer
  • Simplify all of these
    14·2 answers
  • Charlie gathered data about the time it takes him to complete a crossword puzzle and the number of clues in the puzzle. He used
    11·1 answer
  • Solve for x given the lines are parallel.<br> (7x - 8)<br> 62°
    9·1 answer
  • Which point is a solution to the system of equations below?
    8·2 answers
  • How is the space between consecutive whole numbers divided on the number line?
    14·2 answers
  • A city park in the shape of a rectangle measures 90 yards by 120 yards. A rectangular playground inside the park measures 18 yar
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!