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John is shopping for supplies for a coworker's retirement party. Regular sized boxes of forks contain enough for $23$ guests, while value-pack boxes contain enough for $30$ guests. In all, there must be at least enough forks for the $56$ guests who plan to attend. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of regular boxes of forks $\newline$ $y =$ the number of value-packs boxes of forks $\newline$ Choices: $\newline$ (A) $23x + 30y \geq 56$ $\newline$ (B) $30x + 23y \geq 56$ $\newline$ (C) $30x + 23y > 56$ $\newline$ (D) $23x + 30y > 56$

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Write a linear inequality: word problems

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Q. John is shopping for supplies for a coworker's retirement party. Regular sized boxes of forks contain enough for

23

guests, while value-pack boxes contain enough for

30

guests. In all, there must be at least enough forks for the

56

guests who plan to attend.

\newline

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

\newline

x =

the number of regular boxes of forks

\newline

y =

the number of value-packs boxes of forks

\newline

Choices:

\newline

(A)

23x + 30y \geq 56

\newline

(B)

30x + 23y \geq 56

\newline

(C)

30x + 23y > 56

\newline

(D)

23x + 30y > 56

Determine Forks per Box: Determine the amount of forks provided by each type of box. $\newline$ Regular sized boxes provide forks for $23$ guests, and value-pack boxes provide forks for $30$ guests. We need to find an inequality that represents the total number of forks needed for at least $56$ guests.
Define Variables: Define the variables for the number of boxes. $\newline$ Let $x$ be the number of regular boxes of forks, and $y$ be the number of value-pack boxes of forks. The total number of forks needed is the sum of the forks from the regular boxes and the value-pack boxes.
Write Inequality: Write the inequality that represents the total number of forks needed. $\newline$ The inequality will be in the form of $23x + 30y \geq 56$ , where $23x$ represents the forks from the regular boxes and $30y$ represents the forks from the value-pack boxes. The inequality must be greater than or equal to $56$ because John needs to have at least enough forks for $56$ guests.
Choose Correct Inequality: Choose the correct inequality from the given choices. $\newline$ The correct inequality that represents the situation is $23x + 30y \geq 56$ , which corresponds to choice $(D)$ .

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