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A charitable organization in Lanberry is hosting a black tie benefit for charity, and the organization's members hope to bring in at least $\$1,600$ . Standard tickets are available for $\$16$ each, whereas VIP tickets are offered for $\$70$ apiece. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of standard tickets $\newline$ $y =$ the number of VIP tickets $\newline$ Choices: $\newline$ (A) $16x + 70y \leq 1,600$ $\newline$ (B) $16x + 70y \geq 1,600$ $\newline$ (C) $16 + x + 70 + y \leq 1,600$ $\newline$ (D) $16 + x + 70 + y \geq 1,600$

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Write two-variable inequalities: word problems

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Q. A charitable organization in Lanberry is hosting a black tie benefit for charity, and the organization's members hope to bring in at least

\$1,600

. Standard tickets are available for

\$16

each, whereas VIP tickets are offered for

\$70

apiece.

\newline

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

\newline

x =

the number of standard tickets

\newline

y =

the number of VIP tickets

\newline

Choices:

\newline

(A)

16x + 70y \leq 1,600

\newline

(B)

16x + 70y \geq 1,600

\newline

(C)

16 + x + 70 + y \leq 1,600

\newline

(D)

16 + x + 70 + y \geq 1,600

Define variables: Define the variables based on the information given. We are told that $x$ represents the number of standard tickets sold and $y$ represents the number of VIP tickets sold.
Calculate standard revenue: Determine the revenue generated from selling standard tickets. Since standard tickets are sold for $\$16$ each, the total revenue from standard tickets is $16x$ .
Calculate VIP revenue: Determine the revenue generated from selling VIP tickets. Since VIP tickets are sold for $\$70$ each, the total revenue from VIP tickets is $70y$ .
Combine total revenue: Combine the revenues from both standard and VIP tickets to form an expression that represents the total revenue. This gives us $16x + 70y$ .
Set revenue inequality: Since the organization hopes to bring in at least $\$1,600$ , the total revenue from ticket sales must be greater than or equal to $\$1,600$ . This leads us to the inequality $16x + 70y \geq 1,600$ .
Match with choices: Match the inequality from Step $5$ with the given choices. The correct inequality that represents the situation is $(B)16x + 70y \geq 1,600$ .

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