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In order to raise money to attend upcoming competitions, the debate team at Belleville High School is selling apple cider and hot chocolate at a basketball game. They hope to make at least $\$170$ in revenue at tonight's game, with hot chocolate selling for $\$1$ and hot apple cider selling for $\$2$ . $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x$ = the number of hot chocolates sold $\newline$ $y$ = the number of apple ciders sold $\newline$ Choices: $\newline$ A) \(2x + y > $170$ $\newline$ B) \(2x + y \geq $170$ $\newline$ C) x + \(2y > $170$ $\newline$ D) x + \(2y \geq $170$

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Write two-variable inequalities: word problems

Full solution

Q. In order to raise money to attend upcoming competitions, the debate team at Belleville High School is selling apple cider and hot chocolate at a basketball game. They hope to make at least

\$170

in revenue at tonight's game, with hot chocolate selling for

\$1

and hot apple cider selling for

\$2

.

\newline

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

\newline

x

= the number of hot chocolates sold

\newline

y

= the number of apple ciders sold

\newline

Choices:

\newline

A) \(2x + y >

170

\newline

B) \(2x + y \geq

170

\newline

C) x + \(2y >

170

\newline

D) x + \(2y \geq

170

Calculate Revenue per Item: Determine the revenue per item. The debate team sells hot chocolate for $\$1$ each and apple cider for $\$2$ each. Therefore, the revenue from selling $x$ hot chocolates is $\$1$ times $x$ , which is $x$ dollars, and the revenue from selling $y$ apple ciders is $\$2$ times $y$ , which is $2y$ dollars.
Form Total Revenue Expression: Combine the revenues to form an expression for total revenue. The total revenue $R$ from selling $x$ hot chocolates and $y$ apple ciders is the sum of the revenue from each, so $R = x + 2y$ .
Set Revenue Goal Inequality: Set up the inequality based on the goal. The debate team hopes to make at least $\$170$ in revenue. This means the total revenue $R$ must be greater than or equal to $\$170$ . Therefore, the inequality is $x + 2y \geq 170$ .
Match to Given Choices: Match the inequality to the given choices. The inequality we have found is $x + 2y \geq 170$ , which corresponds to choice (D).

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