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

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Answers

Answer:

Answer is C. 9

Step-by-step explanation:

It is basically the same thing as 12-3 and that's equal to 9. It's 9 my man

The distance around a triangle is 36 centimeters. If two sides are equal and the length of the third side is 14 centimeters, what is the length of each of the other two sides?

Answers

Length of unknown side = x

36 = 14 + 2x

Subtract 13 from both sides

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Divide by 2 on both sides to isolate for x

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3. Consider the following box plot.

(a) Find the interquartile range.

(b) What percent of values is included in the interquartile range?

Answers

Answer:

a) Interquartile range= upper quartile- lowwr quartile

= Q3- Q1

= 4.75-2.25

= 2.50

b) ( 2.5 ÷ 6 ) × 100

= 41.67%

Answer:now you can give other guy brainliest.

Step-by-step explanation:

if f(x) = 2x+6 and g(x) = x(3) , what is (g0f)(0)

Answers

Answer:

(g0f)= (2x0+6 x 0x3)= 8x3= 24

Step-by-step explanation:

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Answers

The best answer from the choices provided is option B) 56.

Step-by-step explanation: Simply subtract 34 from 90.

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Answer:

ereee

Step-by-step explanation:

Answer:

c.

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Step-by-step explanation:

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Answer:

(-1,6) is where the point would be.

Just a reflection across the y axis.

Answer:

(-6, 1)

Step-by-step explanation:

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Answers

D. All other choices are wrong

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Answers

Do you have to give me the whole graph lol

Will mark BRAINLIEST!

Find the numeral to put in the blank to make each equation true. Do not convert to base ten. (Hint: In base 12, T stands for the numer 1 greater than 9 and E stands for the number 2 greater than 9.)


a. 4413 five- __five= 2331 five
b. 10011 two+ __ two= 100000 two
c. TEE twelve- __ twelve= 8 twelve
d. 1000 five + __ five = 10000 five

Answers

Answer:

a. 4413₅ - __ ₅ = 2331₅

4413₅ - 2331₅ = 2032₅

b. 10011₂ + __ ₂ = 100000₂

100000₂ - 10011₂ = 10001₂

c. TEE₁₂ - __ ₁₂ = 8₁₂

TEE₁₂ - 8₁₂ = TT3₁₂

d. 1000₅ + __ ₅ = 10000₅

10000₅ - 1000₅ = 4000₅

2 Which expression shows the quotient of 6 and p?
A 6xp
с px6
в 6+ р
D p +6

Answers

Probably d is there is

In a company's first year in operation, it made an annual profit of $322,000. The
profit of the company increased at a constant 21% per year each year. How much
total profit would the company make over the course of its first 26 years of operation,
to the nearest whole number?

Answers

Answer:

Since the annual profit for the FIRST YEAR is $322,000 and it increases 21% every year for 26 years, you do so to find the answer to the question.

Step-by-step explanation:

21% per year

26 years

21 x 26 = 546

Now you have to find 546% of 322,000 and add that to 322,000.

546% of 322,000 is 1,758,120.

hope this helped!

Answer:

$216,265,829

Step-by-step explanation:

To find the sum of a geometric series we use the following equation

[tex]a*\frac{1-r^n}{1-r}[/tex]

we have

[tex]322000*\frac{1-1.21^{26}}{1-1.21}\\\\322000*671.633=216265829[/tex]

Raul recibió un bono de $750, el que era 5% de su salario anual . Su sueldo anual es de ?

Answers

Answer: 375

Step-by-step explanation:

The three side lengths of a triangle are given. Which triangle is a right triangle?

hopefully the text is ok :-)

Answers

Answer:

Triangle A

Explanation:

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Question in link. Please help :(

Answers

Answer:

The median

Step-by-step explanation:

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The growth in per share FCFE of FOX, Inc. is expected to be 10%/year for the next three years, followed by a growth rate of 5%/year for two years; after this five year period, the growth in per share FCFE is expected to be 3%/year, indefinitely. The required rate of return on FOX, Inc. is 12%. Last year's per share FCFE was $1.8. What should the stock sell for today?

Answers

Answer: $25.46

Step-by-step explanation:

Year 1 FCFE = 1.8 * (1 + 10%) = $1.98

Year 2 FCFE = 1.98 * 1.1 = $2.18

Year 3 FCFE = 2.178 * 1.1 = $2.40

Year 4 FCFE = 2.3958 * 1.05 = $2.52

Year 5 FCFE= 2.51559 * 1.05 = ‭2.64

Terminal Value = (2.64 * 1.03) / (12% - 3%)

= $30.21

Now discount all these cashflows to find the value:

= (1.98 / 1.12) + (2.18 / 1.12²) + (2.40 / 1.12³) + (2.52 / 1.12⁴) + (2.64 / 1.12⁵) + (30.21 / 1.12⁵)

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Please help! Like please.

Answers

The answer is letter H

BUILDING PLANS In a scale drawing of a school's floor plan, 6 inches represents 100 feet If the
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Answers

Answer:

10.5

Step-by-step explanation:

You just divide 175/100, and then multiply it by 6 to get 10.5

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Answers

True, true, false, false

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Answers

Answer:

6) 5(1/3)

7) 5(1/3)

8) 3(3/5) or 18/5

because answer were cut off

Answer:

7) 5 [tex]\frac{1}{3} \\[/tex]

8) 5 [tex]\frac{1}{3}[/tex]

9) 3 [tex]\frac{3}{5}[/tex]

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which expression is 1/2 as large as 486-466

Answers

Answer: 20-10

Step-by-step explanation: 486-466 is 20. Half of 20 is 10. Any expression that equals ten is 1/2 as large as 486-466.

The expression is 1/2 as large as 486-466 is with the data 10.

What is fraction?

Fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Let us understand this concept using an example. The following figure shows a pizza that is divided into 8 equal parts. Now, if we want to express one selected part of the pizza, we can express it as 1/8 which shows that out of 8 equal parts, we are referring to 1 part.

Given:

Class = 486 - 466

We have given a class whose upper limit = 486

and, lower limit = 466

the range or difference between class

=486 - 466

=20

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https://brainly.com/question/10354322

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Due today! Why did the "Martian" need a special suit to visit Earth?

Answers

Answer:

But Mars has no magnetosphere, and its atmosphere is over 100 times thinner than Earth's atmosphere. The trip to Mars and the stay on Mars will mean extended radiation exposure. Astronauts will need special habitats, suits, and machines that will protect them from radiation, which otherwise could cause cancer.

Step-by-step explanation:

0.8km need to be convert into hour an minute please help

Answers

Answer:

It is not possible

Step-by-step explanation:

Required

Convert 0.8km to hours and minutes

One of the condition for a successful conversion is that: only units of the same metric can be converted.

i.e.

Meters can be converted to feet (they both measure distance)

Days can be converted to years (they both measure time)

Pounds can be converted to grams (they both measure weight)

But in the given question, you attempt to convert from distance to time.

This is not possible, because time and distance are different measurements

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Answers

1. 1.25

2. 0.85

3. 0.2

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Answers

Answer:

3b+10

Step-by-step explanation:

The expression is not factorable with rational numbers.

3b+10

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Answers

Answer:

1.6 m = 5.3 ft

∠A and \angle B∠B are complementary angles. If m\angle A=(x+10)^{\circ}∠A=(x+10)

and m\angle B=(3x+28)^{\circ}∠B=(3x+28)

, then find the measure of \angle B∠B.

Answers

Answer:

x + 10 + 3x + 28 = 90

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x= 13

Step-by-step explanation:

Angle B = 67

Is this a Percent Increase or Decrease Problem?
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Answers

Answer:

Percent Decrease

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help pleaseee !!! im stuck

Answers

9514 1404 393

Answer:

102 cm²232 in²40.46 ft²480 mm²

Step-by-step explanation:

The first three cuboid prisms all use the same area formula:

  A = 2(LW +H(L+W))

__

1. A = 2(3·3 +7(3+3)) = 2(9 +42) = 102 . . . cm²

2. A = 2(2·8 +10(2 +8)) = 2(16 +100) = 232 . . . in²

3. A = 2(4.9·3 +0.7(4.9 +3)) = 2(14.7 +5.53) = 40.46 . . . ft²

__

4. The area of this prism is the total of the area of the two triangular bases  and the areas of the rectangular faces. For triangle legs a, b and hypotenuse c, and prism depth d, the area formula can be written as ...

  A = ab +d(a+b+c)

  A = (8 mm)(15 mm) +(9 mm)(8 mm + 15 mm + 17 mm)

  A = (120 +9(40)) mm² = 480 mm²

I am not sure how to solve these equations. Can someone please help me?

Answers

Answer: 1. 1.14142842 (sorry this is what i got)

               2.  -13.14142842

Step-by-step explanation:

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