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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\$170 in revenue at tonight's game, with hot chocolate selling for $1\$1 and hot apple cider selling for $2\$2.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinexx = the number of hot chocolates sold\newlineyy = the number of apple ciders sold\newlineChoices:\newlineA) \(2x + y > 170170\newlineB) \(2x + y \geq 170170\newlineC) x + \(2y > 170170\newlineD) x + \(2y \geq 170170

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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\$170 in revenue at tonight's game, with hot chocolate selling for $1\$1 and hot apple cider selling for $2\$2.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinexx = the number of hot chocolates sold\newlineyy = the number of apple ciders sold\newlineChoices:\newlineA) \(2x + y > 170170\newlineB) \(2x + y \geq 170170\newlineC) x + \(2y > 170170\newlineD) x + \(2y \geq 170170
  1. Calculate Revenue per Item: Determine the revenue per item. The debate team sells hot chocolate for $1\$1 each and apple cider for $2\$2 each. Therefore, the revenue from selling xx hot chocolates is $1\$1 times xx, which is xx dollars, and the revenue from selling yy apple ciders is $2\$2 times yy, which is 2y2y dollars.
  2. Form Total Revenue Expression: Combine the revenues to form an expression for total revenue. The total revenue RR from selling xx hot chocolates and yy apple ciders is the sum of the revenue from each, so R=x+2yR = x + 2y.
  3. Set Revenue Goal Inequality: Set up the inequality based on the goal. The debate team hopes to make at least $170\$170 in revenue. This means the total revenue RR must be greater than or equal to $170\$170. Therefore, the inequality is x+2y≥170x + 2y \geq 170.
  4. Match to Given Choices: Match the inequality to the given choices. The inequality we have found is x+2y≥170x + 2y \geq 170, which corresponds to choice (D).

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