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An event planner, is ordering centerpieces and garlands for a holiday party. Each garland costs $\$42$ and each centerpiece costs $\$9$ . 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) $42x + 9y < 650$ $\newline$ (B) $42x + 9y \leq 650$ $\newline$ (C) $42x + 9y \geq 650$ $\newline$ (D) $42x + 9y > 650$

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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

\$42

and each centerpiece costs

\$9

. 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)

42x + 9y < 650

\newline

(B)

42x + 9y \leq 650

\newline

(C)

42x + 9y \geq 650

\newline

(D)

42x + 9y > 650

Garland Cost Calculation: We know: $\newline$ Cost of each garland: $\$42$ $\newline$ Number of garlands ordered: $x$ $\newline$ What is the total cost of the garlands? $\newline$ Cost of each garland $\times$ Number of garlands $\newline$ $= 42 \times x$ $\newline$ $= 42x$ $\newline$ Total cost of garlands: $42x$
Centerpiece Cost Calculation: We know: $\newline$ Cost of each centerpiece: $\$9$ $\newline$ Number of centerpieces ordered: $y$ $\newline$ What is the total cost of the centerpieces? $\newline$ Cost of each centerpiece $\times$ Number of centerpieces $\newline$ $= 9 \times y$ $\newline$ $= 9y$ $\newline$ Total cost of centerpieces: $9y$
Total Cost Calculation: We know: $\newline$ Total cost of garlands: $42x$ $\newline$ Total cost of centerpieces: $9y$ $\newline$ What is the total cost of garlands and centerpieces? $\newline$ Add total cost of garlands and centerpieces. $\newline$ $42x + 9y$
Budget Inequality: We know: $\newline$ Total cost of garlands and centerpieces: $42x + 9y$ $\newline$ Event planner's floral budget: No more than $\$650$ $\newline$ Select the inequality that describes this situation. $\newline$ Total cost must be less than or equal to $650$ . $\newline$ Inequality: $42x + 9y \leq 650$

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