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
Ratling [72]
3 years ago
11

An arena that hosts sporting events and concerts has three sections for 3 levels of seating. For a basketball game seats in Sect

ion A cost $100, seats in section B cost $50 and seats in section C cost $35. The number of seats in section C equals the number of seats in sections A and B combined. The arena holds 12,000 seats and the game is sold out. If the total revenue from ticket sales is $560,000, determine the number of seats in each section.
Start by assigning your variables. Then write your system of equations. Solve using substitution or elimination. Show all work for this system of 3 equations.
Mathematics
2 answers:
Usimov [2.4K]3 years ago
8 0

Answer:

There are 1000 seats in Section A, 5000 seats in section B and 6000 seats in Section C.

Step-by-step explanation:

Let the number of seats in Section A=x

Let the number of seats in Section B=y

Let the number of seats in Section C=z

The number of seats in section C equals the number of seats in sections A and B combined.

z=x+y......(I)

The arena holds 12,000.

x+y+z=12000......(II)

For a basketball game seats in Section A cost $100, seats in section B cost $50 and seats in section C cost $35.

Total revenue from ticket sales is $560,000

100x+50y+35z=560000.....(III)

The system of equation is given as:

z=x+y......(I)

x+y+z=12000......(II)

100x+50y+35z=560000.....(III)

Substitute z=x+y From (I) into Equation (II)

x+y+x+y=12000

2x+2y=12000

x+y=6000......(IV)

Substitute z=x+y From (I) into (III).

100x+50y+35(x+y)=560000

100x+35x+50y+35y=560000

135x+85y=560000.....(V)

From (IV), x=6000-y

135(6000-y)+85y=560000

810000-135y+85y=560000

50y=250000

y=5000

Recall From (IV), x=6000-y

x= 6000-5000=1000

From (I)

z=x+y=1000+5000=6000

There are 1000 seats in Section A, 5000 seats in section B and 6000 seats in Section C.

igor_vitrenko [27]3 years ago
4 0

Answer: section A has 1000 seats

Section B has 5000 seats and section C has 6000 seats

Step-by-step explanation:

Lety use "A" to represent the number of seats in section A, "B" to represent the number of seats in section B and "C" to represent the number of seats in section C.

Since the number of seats in section C equals the number of seats in section A and B combined, then:

A+B = C -------eqn 1

Again, the arena holds 12,000 seats.

So, A+B+C = 12,0000 --------eqn 2

Recall that seats in section A costs $100. Seat B costs $50 and seat C costs $35. If the game is sold out and the total revenue generated from ticket sales is $560,000.

Then:. (100×A)+(50×B)+(35×C)= $560,000

100A+50B+35C= 560,000 ---------eqn 3

Since A+B = C (in eqn 1), we substitute "A+B" for C in eqn 2

Therefore C + C = 12,000

2C = 12,000

C = 6,000 seats.

If C is equal to 6000, we then substitute C for 6000 seats in eqn 1

Therefore, A+B = 6,000

B= 6000 - A

We then substitute "B" for "6,000 - A" and "C" for 6000 in equation 3

100A + [50 × (6000 - A)]+ (35 × 6000) = 560,000

100A + (300,000 - 50A) + 210,000 = 560,000

50A + 510000 = 560000

50A = 50000

A = 1,000 seats

Substitute "A" for 1000 and "C" for 6000 in eqn 1

Therefore: 1000 + B = 6000

B = 6000 - 1000

B = 5000 seats

Summarily, there are 1,000 seats in section A; 5,000 seats in section B and 6000 seats in section C

You might be interested in
The coordinate grid shows triangle STU.
vladimir2022 [97]

Answer:The rule for a rotation by 270° about the origin is (x,y)→(y,−x) .

YOUR ANSWER IS B

Step-by-step explanation:

4 0
3 years ago
20 points
gavmur [86]

Answer:

Michael buys 800 hockey cards from jackson

6 0
2 years ago
Read 2 more answers
3x-1=5x+10. and the X= -5 1/2
irga5000 [103]

Answer:

The answer is 1 or infinite solutions

Step-by-step explanation:

When you plug in the value of -5.5 into the equation, you will eventually end up with -17.5=-17.5, making the answer infinite or 1.

7 0
2 years ago
HELP PLEASE! 50 POINTS, WILL MARK BRAINLIEST WHOEVER IS FIRST!
Temka [501]

95

Step-by-step explanation:

she would have to get At Least 95 or better to balance it out

4 0
3 years ago
2 1
iragen [17]
A. (8,4) because you can tell in the second pattern
8 0
3 years ago
Other questions:
  • Will give brainlist**** What is the slope-intercept equation for the cost of a sub at Fred’s Sub Shop?
    9·1 answer
  • A school contains 357 boys and 323 girls.
    13·1 answer
  • What is 970+12% of the amount over 9,700
    7·1 answer
  • Order 3/2, 5/8, 9/4, 1 & 7/8 from least to greatest
    9·1 answer
  • Find an equivalent fractions for each given fraction 4/10
    10·1 answer
  • If Company X has 1600 employees and 80% of those employees have attended the warehouse training course how many employees have y
    12·1 answer
  • Solve the equation graphically by finding intersections.<br> |2x+1|=17<br> X=
    5·1 answer
  • A number that is the 3 times table an 7 times table between 364 and 384
    5·2 answers
  • Please help(: I’ll be posting more I just wanna pass
    14·1 answer
  • 8th Grade Math Homework Thursday, January 28th
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!