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An event planner wants to order some ice sculptures as decorations for a company party. Small sculptures cost $\$150$ and large sculptures cost $\$330$ , and the maximum budget for this portion of the party is $\$2,300$ . $\newline$ 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 $\newline$ $\newline$ Choices: $\newline$ (A) $150x - 330y \leq 2,300$ $\newline$ (B) $150x + 330y \geq 2,300$ $\newline$ (C) $150x + 330y \leq 2,300$ $\newline$ (D) $150x - 330y \geq 2,300$

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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

\$330

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

\$2,300

.

\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

\newline

Choices:

\newline

(A)

150x - 330y \leq 2,300

\newline

(B)

150x + 330y \geq 2,300

\newline

(C)

150x + 330y \leq 2,300

\newline

(D)

150x - 330y \geq 2,300

Determine Costs and Variables: 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: $\$330$ $\newline$ Number of large ice sculptures: $y$
Calculate Total Cost: Calculate the total cost for a given number of small and large ice sculptures. $\newline$ Total cost for small ice sculptures: $150x$ $\newline$ Total cost for large ice sculptures: $330y$ $\newline$ Total cost for all ice sculptures: $150x + 330y$
Apply Budget Constraint: Apply the budget constraint to the total cost. $\newline$ The maximum budget for ice sculptures is $\$2,300$ , so the total cost of small and large ice sculptures combined must be less than or equal to this amount. $\newline$ Inequality: $150x + 330y \leq 2,300$

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