Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

An event planner wants to order some ice sculptures as decorations for a company party. Small sculptures cost $\$150$ and large sculptures cost $\$370$ , and the maximum budget for this portion of the party is $\$2,200$ . $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of small ice sculptures $\newline$ $y =$ the number of large ice sculptures $\newline$ Choices: $\newline$ (A) $150x + 370y \geq 2,200$ $\newline$ (B) $150 + x + 370 + y \leq 2,200$ $\newline$ (C) $150 + x + 370 + y \geq 2,200$ $\newline$ (D) $150x + 370y \leq 2,200$

View step-by-step help

View step-by-step help

Write a linear inequality: word problems

Full solution

Q. An event planner wants to order some ice sculptures as decorations for a company party. Small sculptures cost

\$150

and large sculptures cost

\$370

, and the maximum budget for this portion of the party is

\$2,200

.

\newline

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

\newline

x =

the number of small ice sculptures

\newline

y =

the number of large ice sculptures

\newline

Choices:

\newline

(A)

150x + 370y \geq 2,200

\newline

(B)

150 + x + 370 + y \leq 2,200

\newline

(C)

150 + x + 370 + y \geq 2,200

\newline

(D)

150x + 370y \leq 2,200

Determine Costs: Determine the cost of each type of ice sculpture and the variables associated with them. $\newline$ Cost of each small ice sculpture: $\$150$ $\newline$ Number of small ice sculptures: $x$ $\newline$ Cost of each large ice sculpture: $\$370$ $\newline$ Number of large ice sculptures: $y$
Calculate Small Ice: Calculate the total cost for the small ice sculptures. $\newline$ Total cost for small ice sculptures = Cost of each small ice sculpture $\times$ Number of small ice sculptures $\newline$ = $\$(150) \times x$ $\newline$ = $150x$
Calculate Large Ice: Calculate the total cost for the large ice sculptures. $\newline$ Total cost for large ice sculptures = Cost of each large ice sculpture $\times$ Number of large ice sculptures $\newline$ = $\$(370) \times y$ $\newline$ = $370y$
Combine Total Costs: Combine the total costs for both small and large ice sculptures to represent the total expenditure. $\newline$ Total expenditure = Total cost for small ice sculptures + Total cost for large ice sculptures $\newline$ = $150x + 370y$
Determine Budget Constraint: Determine the budget constraint for the total expenditure. $\newline$ Maximum budget for ice sculptures: $\$2,200$ $\newline$ The total expenditure must be less than or equal to the maximum budget. $\newline$ Inequality: $150x + 370y \leq 2,200$

More problems from Write a linear inequality: word problems

Question

s

\newline

|s| + 3 \geq 8

\newline

\newline

Write a compound inequality like

1 < x < 3

x < 1

x > 3

. Use integers, proper fractions, or improper fractions in simplest form.

\newline

\newline

Posted 1 month ago

Question

x

\newline

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

\newline

\newline

Write a compound inequality like

1 < x < 3

x < 1

x > 3

\newline

Posted 1 month 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 1 month 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 4 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 4 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 1 month 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 26 days 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 4 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 2 months ago