The local theater has three types of seats for Broadway plays: main floor, balcony, and mezzanine. Main floor tickets are $48, balcony tickets are $45, and mezzanine tickets are $34. One particular night, sales totaled $65,140. There were 381 more main floor tickets sold than balcony and mezzanine tickets combined. The number of balcony tickets sold is 328 more than 2 times the number of mezzanine tickets sold. How many of each type of ticket were sold?
I already have these equations: 48x+45y+34z=65140, x=y+z+381, y=2x+328, but I can't figure out how to substitute them.

Answers

Answer 1

Answer: In this problem, you have three unknowns: broadway tickets for the (1) main floor, (2) balcony and (3) mezzanine. To solve algebraic equations, the total number of unknowns must be the same with the number of independent equations. With that, let's formulate these three equations.

Let the 3 unknowns be

x = number of tickets for the main floor

y = number of tickets for the balcony

z = number of tickets for the mezzanine

The independent equations are:

59x+50y+40z=73,785 --> eq 1

x = y+z+435 --> eq 2

y = 78 + 33 z ---> eq 3

Solve the equations simultaneously. Substitute eq3 to eq 2

x = 78+33z+z+435

x = 513+34z --> eq 4

Substitute eq 4 and eq 3 to eq 1

59(513+34z)+50( 78 + 33 z)+40z=73,785

Solve for z using the calculator: z = 11

Use eq 4 to find x: x = 877

Use eq 2 to find y: y = 432

There were 877 main floor tickets, 432 balcony tickets and 11 mezzanine tickets sold.

Step-by-step explanation:

Answer 2

Answer:

Main floor - 892, balcony - 450, mezzanine- 61

Step-by-step explanation:

Main floor - x, balcony - y, mezzanine- z

Equations:

48x + 45y + 34z = 65140            ↔ (1)x = 381 + y + z                              ↔ (2)y = 2z + 328                                 ↔ (3)

Substitute (3) into (2):

x = 381 + 2z + 328 + z  ⇒ x = 3z + 709                                 ↔ (4)

Substitute (2) and (4) into (1) and solve for z:

48(3z + 709) + 45(2z + 328) + 34z = 65140144z + 48*709 + 90z + 45*328 + 34z = 65140268z + 34032 + 14760 = 65140268z = 65140 - 48792268z = 16348z = 16348/268z = 61

Find x and y:

x = 3z + 709 = 3*61 + 709 = 892y = 2z + 328 = 2*61 + 328 = 450


Related Questions

Alex is saving money at a constant rate. Suppose she initially has $170 saved, and after 5 months, she has $420 saved.
Which of these expresses the rate at which Alex is saving?

Answers

Answer:

50 dollars per month

Step-by-step explanation:

Money saved over time period x / Time period x = $250/5 months=$50/1 month

According to this diagram, what is tan 62°?
62°
17
8
280
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O A.
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Answer:

Geoff planted dahlias in his garden. Dahlias have bulbs that divide and reproduce underground. In the first year, Geoff's garden produced 4 bulbs. In the second year, it produced 8 bulbs, and in the third year, it produced 16 bulbs

Step-by-step explanation:

Kelly paid $45.36 for a sweater that was on sale for 25% off the original price. She paid 8% sales tax on the sale price.

What was the original price of the sweater, in dollars​

Answers

The sales tax is determined by computing a percent of the purchase price. To find the sales tax multiply the purchase price by the sales tax rate. Remember to convert the sales tax rate from a percent to a decimal number. Once the sales tax is calculated, it is added to the purchase price.

Step-by-step explanation: Sorry if this doesn't help....

Area = ???????????????

Answers

Answer:

x^2+10x+21

Step-by-step explanation:

Blue box: x*x=x^2

Green box: x*3=3x

Purple box: 7*x=7x

Orange box: 7*3=21

x^2+(3x+7x)+21

Combine like term

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1) The endpoints of AB are A(-3, 8) and B(4,5). If AB is
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Answers

Answer:

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A chi-square test of independence was conducted to investigate whether there is an association between the location where a person lives in a city (north, south, east, or west) and who the person planned to vote for in the upcoming mayoral election (the incumbent or the challenger). A random sample of 100 potential voters was selected, and the hypothesis test had a chi-square test statistic of χ2=9.84 with a p-value of 0.02. Which of the following statements is the correct interpretation of the p-value in context?

(A) There is a 2 percent chance that where a person lives and who that person plans to vote for are independent.

(B) There is a 2 percent chance that where a person lives and who that person plans to vote for are dependent.

(C) There is a 2 percent chance of making a Type II error.

(D) Assuming that the location of where a person lives and who that person plans to vote for are dependent, there is a 2 percent chance of finding a test statistic that is 9.84 or greater.

(E) Assuming that the location of where a person lives and who that person plans to vote for are independent, there is a 2 percent chance of finding a test statistic that is 9.84 or greater.

Answers

Answer:

E) Assuming that the location of where a person lives and who that person plans to vote for are independent, there is a 2 percent chance of finding a test statistic that is 9.84 or greater.

Step-by-step explanation:

Chegg

When Janelle was born, her grandmother put $200 into a college savings account for her. Each month, her grandmother adds $50 to the account. Which inequality can be used to find m, the number of months it will take for Janelle’s savings account to have more than $1,250 in savings?

Answers

it would take 21 months for her to have exactly 1250

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Answers

Answer:

25 friends

Step-by-step explanation:

79 - 4 = 75.

75 ÷ 3 = 25

25 friends

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Answers

9514 1404 393

Answer:

  -21, 13

Step-by-step explanation:

If Z is located to the right of Y, its point on the number line is -4+17 = 13.

If Z is located to the left of Y, its point on the number line is -4-17 = -21.

There are two possible locations for Z on a number line.

_____

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In 3-dimensions, the set of points becomes a sphere with radius 17.

Jeremy spent $33 on 3 CDs. At This rate. how much would 6 CDs cost ?​

Answers

It would cost $66.

33/3=11.
It costs $11 per CD.
6*11=66.
It would be $66 for 6 CDs.

Answer:

It would cost Jeremy $66 for 6 CDs

Step-by-step explanation:

3 CDs for $33

3(2)=6

$33(2)=$66

Which is a measure of the efficiency of an investment?
A.efficiency cocfficient
B.return on investment
C.return rato

Answers

Answer:

B. return on investment

Step-by-step explanation:

Return on Investment (ROI) is a performance measure used to evaluate the efficiency of an investment or compare the efficiency of a number of different investments.

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sold during the second day?

Answers

Answer:

On the second day, 50% of the total computer inventory was sold.

Step-by-step explanation:

Since during a sale of computers, one-fourth of the inventory was sold the first day, while the next day two-thirds of the remaining inventory was sold, to determine what percent of the total inventory was sold during the second day, we must perform the following calculations:

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Answers

Step-by-step explanation:

We have four fundamental operations on integers. They are addition, subtraction, multiplication, and division.

hasann please help me

Answers

Don’t believe the link^

Answer:

The length and width and height is already given.

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Width is: 1 1/2

Height is: 2 1/2

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Can someone please give me the answer I will mark u brilliant

Answers

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Step-by-step explanation:

First Solid

V= l*w*h

V= 5/8*3/4*2

V= 15/16

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Second Solid

V= l*w*h

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V=  7/4

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Answers

Answer:

It is important because it allows you to calculate the surface area of a trapezoidal prism

Step-by-step explanation:

Log 64 = x. Find X

Answers

Answer:

3

Step-by-step explanation:

Rewrite the logarithmic notation to index notation.

4^x=64

Change 64 to index notation

ie 64 = 4^3

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I think you it already Bc the other person put it

1/4 / (17 + 4)
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Answers

Answer:

0.0119047619

Step-by-step explanation:

Answer:

21/4

Step-by-step explanation:

1/4 ÷ (17 + 4)

1/4 ÷ (21)

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-TheUnknownScientist

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Answers

Answer:

-6.87

Consider the opposite symbol

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Answers

Answer:

2 more sides.

Step-by-step explanation:

Decagon = 10 sides

Octagon = 8 sides

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Answer:

2 sides.

Step-by-step explanation:

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Answers

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Step-by-step explanation:

#7

This is an isosceles triangle, so the angles formed at the base of the congruent sides are equal.

5x-7=8x-55

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16=x

#9

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Pick a random answer

The size your dog and the number of times you take it to the vet, The amount your drive to school and the amount you have to pay for gas, The number of people at your party and the number of sodas you have in the refrigerator. What correlation are all of these. None, Positive, or Negative thanks so much.

Answers

1. No correlation

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2. Positive correlation

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3. Negative correlation

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Answers

Answer:

76 is the answer

Step-by-step explanation:

4³+6(2)

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76

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7 mi

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1

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Answers

Área # 56 sq mi
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have a good day

Answers

Answer:

Thank you, thank you, thank you *bows head* ✌️❤️

[tex] \infty \infty [/tex]

Answer:

Yay points

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(*/_÷)

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Answers

Answer:

33

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation: Hope this helps Have a good day :)

HEEEEEEEEEEEEEELLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPPP

Answers

The answer above is scam. They just tyr to get potns. The correct andwr dos 3736.

Answer:

triangle and cylinder is your answer

simplify
[tex] {a}^{2} - {b}^{2} [/tex]

Answers

Answer:

a² - b²

= (a+b) (a-b)

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