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A sculptor is selling her work at an exhibit and hopes to earn at least $\$28,000$ in revenue. Small pieces go for $\$480$ and large pieces go for $\$1,500$ . Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $x =$ the number of small pieces sold $y =$ the number of large pieces sold $\newline$ Choices: $\newline$ (A) $480x + 1,500y \geq 28,000$ $\newline$ (B) $1,500x + 480y \leq 28,000$ $\newline$ (C) $1,500x + 480y \geq 28,000$ $\newline$ (D) $480x + 1,500y \leq 28,000$

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Write a linear inequality: word problems

Full solution

Q. A sculptor is selling her work at an exhibit and hopes to earn at least

\$28,000

in revenue. Small pieces go for

\$480

and large pieces go for

\$1,500

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

x =

the number of small pieces sold

y =

the number of large pieces sold

\newline

Choices:

\newline

(A)

480x + 1,500y \geq 28,000

\newline

(B)

1,500x + 480y \leq 28,000

\newline

(C)

1,500x + 480y \geq 28,000

\newline

(D)

480x + 1,500y \leq 28,000

Calculate Small Piece Revenue: Determine the revenue from selling one small piece. $\newline$ Revenue from one small piece: $\$480$ $\newline$ Number of small pieces sold: $x$ $\newline$ Total revenue from small pieces: $480 \times x = 480x$
Calculate Large Piece Revenue: Determine the revenue from selling one large piece. $\newline$ Revenue from one large piece: $\$1,500$ $\newline$ Number of large pieces sold: $y$ $\newline$ Total revenue from large pieces: $1,500 \times y = 1,500y$
Combine Revenues: Combine the revenues from small and large pieces to form an expression for total revenue. $\newline$ Total revenue from small and large pieces: $480x + 1,500y$
Formulate Inequality: Formulate the inequality based on the sculptor's goal. $\newline$ The sculptor hopes to earn at least $\$28,000$ , which means the total revenue must be greater than or equal to $\$28,000$ . $\newline$ Inequality: $480x + 1,500y \geq 28,000$

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