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A motel is purchasing new towels. Suites require $12$ towels and individual rooms require $4$ towels. The minimum order required by the towel vendor is $664$ towels. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of suites receiving new towels $\newline$ $y =$ the number of individual rooms receiving new towels $\newline$ Choices: $\newline$ (A) $12x + 4y > 664$ $\newline$ (B) $12x \times 4y \geq 664$ $\newline$ (C) $12x + 4y \geq 664$ $\newline$ (D) $12x \times 4y > 664$

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Write a linear inequality: word problems

Full solution

Q. A motel is purchasing new towels. Suites require

12

towels and individual rooms require

4

towels. The minimum order required by the towel vendor is

664

towels.

\newline

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

\newline

x =

the number of suites receiving new towels

\newline

y =

the number of individual rooms receiving new towels

\newline

Choices:

\newline

(A)

12x + 4y > 664

\newline

(B)

12x \times 4y \geq 664

\newline

(C)

12x + 4y \geq 664

\newline

(D)

12x \times 4y > 664

Calculate Total Towels for Suites: Determine the total number of towels needed for suites. $\newline$ We know: $\newline$ Number of towels needed per suite: $12$ $\newline$ Number of suites: $x$ $\newline$ What is the total number of towels needed for suites? $\newline$ Number of towels per suite $\times$ Number of suites $\newline$ = $12 \times x$ $\newline$ = $12x$ $\newline$ Total number of towels for suites: $12x$
Calculate Total Towels for Rooms: Determine the total number of towels needed for individual rooms. $\newline$ We know: $\newline$ Number of towels needed per individual room: $4$ $\newline$ Number of individual rooms: $y$ $\newline$ What is the total number of towels needed for individual rooms? $\newline$ Number of towels per room $\times$ Number of rooms $\newline$ = $4 \times y$ $\newline$ = $4y$ $\newline$ Total number of towels for individual rooms: $4y$
Combine Total Towels: Combine the total number of towels needed for suites and individual rooms. $\newline$ We know: $\newline$ Towels for suites: $12x$ $\newline$ Towels for individual rooms: $4y$ $\newline$ What is the total number of towels needed for both suites and individual rooms? $\newline$ Add total number of towels for suites and individual rooms. $\newline$ $12x + 4y$
Determine Minimum Order Inequality: Determine the inequality that represents the minimum order requirement. $\newline$ We know: $\newline$ Total number of towels: $12x + 4y$ $\newline$ Minimum order required by the vendor: At least $664$ towels $\newline$ Select the inequality that describes this situation. $\newline$ Total number of towels must be greater than or equal to $664$ . $\newline$ Inequality: $12x + 4y \geq 664$

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