Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The Oakland City Ballet is selling tickets for an upcoming performance, and the ballet company hopes to bring in at least $\$5,900$ in revenue. Regular tickets cost $\$49$ , whereas discounted tickets cost $\$23$ . Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $x =$ the number of regular tickets sold $y =$ the number of discounted tickets sold $\newline$ Choices: $\newline$ (A) $49x + 23y \leq 5,900$ $\newline$ (B) $49 + x + 23 + y \leq 5,900$ $\newline$ (C) $49 + x + 23 + y \geq 5,900$ $\newline$ (D) $49x + 23y \geq 5,900$

View step-by-step help

View step-by-step help

Write a linear inequality: word problems

Full solution

Q. The Oakland City Ballet is selling tickets for an upcoming performance, and the ballet company hopes to bring in at least

\$5,900

in revenue. Regular tickets cost

\$49

, whereas discounted tickets cost

\$23

. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

x =

the number of regular tickets sold

y =

the number of discounted tickets sold

\newline

Choices:

\newline

(A)

49x + 23y \leq 5,900

\newline

(B)

49 + x + 23 + y \leq 5,900

\newline

(C)

49 + x + 23 + y \geq 5,900

\newline

(D)

49x + 23y \geq 5,900

Calculate Regular Ticket Revenue: Determine the revenue from selling one regular ticket. $\newline$ Revenue from one regular ticket = $\$49$ $\newline$ Number of regular tickets sold = $x$ $\newline$ Total revenue from regular tickets = $49 \times x = 49x$
Calculate Discounted Ticket Revenue: Determine the revenue from selling one discounted ticket. $\newline$ Revenue from one discounted ticket = $\$23$ $\newline$ Number of discounted tickets sold = $y$ $\newline$ Total revenue from discounted tickets = $23 \times y = 23y$
Combine Regular and Discounted Revenue: Combine the revenues from regular and discounted tickets to form an expression for total revenue. $\newline$ Total revenue = Revenue from regular tickets + Revenue from discounted tickets $\newline$ Total revenue = $49x + 23y$
Formulate Revenue Inequality: Formulate the inequality based on the company's goal. $\newline$ The company hopes to bring in at least $\$5,900$ in revenue. $\newline$ This means the total revenue should be greater than or equal to $\$5,900$ . $\newline$ Inequality: $49x + 23y \geq 5,900$

More problems from Write a linear inequality: word problems

Question

s

\newline

|s| + 3 \geq 8

Posted 4 months ago

Question

Which compound inequality represents the value of

x ?

\newline

(x - 1)(x + 1) > 0

\newline

Posted 4 months ago

Question

A particular company charges advertisers a one time cost of

\$500

, in addition to

\$4.50

for every one thousand times an advertisement is shown on the company's webpage. An advertiser wants its ad to appear

M

thousand times on the webpage, but does not want to spend more than

\$5,000

. Which of the following inequalities best describes the situation?

\newline

\newline

500+4.50M\geq5,000

\newline

4.50+500M>5,000

\newline

500+4.50M\leq5,000

\newline

500+4.50M<5,000

Posted 7 months ago

Question

7x+1 < x+9

\newline

Which of the following best describes the solutions to the inequality shown?

\newline

1

\newline

x > \frac{4}{3}

\newline

x < \frac{4}{3}

\newline

x < 1

\newline

x < \frac{5}{3}

Posted 4 months ago

Question

52-3x < -14

\newline

Which of the following best describes the solutions to the inequality shown?

\newline

1

\newline

x > -\frac{38}{3}

\newline

x > \frac{38}{3}

\newline

x < 22

\newline

x > 22

Posted 10 months ago

Question

5-3x > 2x+2

\newline

Which of the following best describes the solutions to the inequality shown?

\newline

1

\newline

x < \frac{7}{5}

\newline

x < 3

\newline

x < \frac{3}{5}

\newline

x > \frac{3}{5}

Posted 10 months ago

Question

Rani is a real estate agent. For each house she sells, she pays

\$ 100

in fees, but earns a commission of

1.8 \%

of the selling price of the house. Rani's total profit from a particular house is

\$ 4,580

p

represents the selling price of the house, which equation best models the situation?

\newline

1

\newline

0.018 p-100=4580

\newline

0.018 p+100=4580

\newline

(100-0.018) p=4580

\newline

(100+0.018) p=4580

Posted 8 months ago

Question

A commercial airplane that is

1

500

2

500

-mile journey is traveling at

450

knots in still air when it picks up a tailwind of

150

knots (in the same direction). If

h

is the number of hours remaining in the airplane's flight, which of the following equations best describes the situation?

\newline

1

\mathrm{knot}=1.15

miles per hour (mph)

\newline

1

\newline

1,500+690 h=2,500

\newline

1,500+600 h=2,500

\newline

1,500-600 h=2,500

\newline

1,500-690 h=2,500

Posted 7 months ago

Question

A weeping willow that is

15

feet in height grows to a maximum height of

35

y

years at a constant rate of

24

inches per year. Which of the following equations best describes this situation?

\newline

1

=12

\newline

1

\newline

35=15+2 y

\newline

35=15+24 y

\newline

35=15-2 y

\newline

35=15-24 y

Posted 10 months ago

Question

The gas mileage for a car is

23

miles per gallon when the car travels at

60

miles per hour. The car begins a trip with

13

gallons in its tank, travels at an average speed of

60

miles per hour for

h

hours, and ends the trip with

10

gallons in its tank. Which of the following equations best models this situation?

\newline

1

\newline

13-\frac{23 h}{60}=10

\newline

13-\frac{60 h}{23}=10

\newline

\frac{13-60 h}{23}=10

\newline

\frac{13-23 h}{60}=10

Posted 8 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant