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An event planner, is ordering centerpieces and garlands for a holiday party. Each garland costs $\$36$ and each centerpiece costs $\$10$ . The planner has been given a total floral budget of no more than $\$650$ . $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of garlands ordered $\newline$ $y =$ the number of centerpieces ordered $\newline$ Choices: $\newline$ (A) 36x + 10y < 650 $\newline$ (B) $36x + 10y \leq 650$ $\newline$ (C) 10x + 36y < 650 $\newline$ (D) $10x + 36y \leq 650$

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Write a linear inequality: word problems

Full solution

Q. An event planner, is ordering centerpieces and garlands for a holiday party. Each garland costs

\$36

and each centerpiece costs

\$10

. The planner has been given a total floral budget of no more than

\$650

.

\newline

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

\newline

x =

the number of garlands ordered

\newline

y =

the number of centerpieces ordered

\newline

Choices:

\newline

(A)

36x + 10y < 650

\newline

(B)

36x + 10y \leq 650

\newline

(C)

10x + 36y < 650

\newline

(D)

10x + 36y \leq 650

Determine Cost Variables: Determine the cost per item and the variables associated with them. $\newline$ Cost of each garland: $\$36$ $\newline$ Number of garlands ordered: $x$ $\newline$ Cost of each centerpiece: $\$10$ $\newline$ Number of centerpieces ordered: $y$
Calculate Garland Cost: Calculate the total cost for the garlands. $\newline$ Total cost for garlands = Cost of each garland $\times$ Number of garlands $\newline$ = $36 \times x$ $\newline$ = $36x$
Calculate Centerpiece Cost: Calculate the total cost for the centerpieces. $\newline$ Total cost for centerpieces = Cost of each centerpiece $\times$ Number of centerpieces $\newline$ $= 10 \times y$ $\newline$ $= 10y$
Combine Total Costs: Combine the total costs to form an expression for the total floral budget. $\newline$ Total floral budget = Total cost for garlands + Total cost for centerpieces $\newline$ = $36x + 10y$
Budget Inequality: The event planner has a budget of no more than \$\(650\). This means the total cost must be less than or equal to \$\(650\).\(\newline\)Inequality: \(36x + 10y \leq 650\)

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