In order to raise money to attend upcoming competitions, the debate team at Dover High School is selling apple cider and hot chocolate at a basketball game. They hope to make at least $250 in revenue at tonight's game, with hot chocolate selling for $1 and hot apple cider selling for $2.

Question

Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of hot chocolates sold
y = the number of apple ciders sold

Answer 1

To express the revenue from selling hot chocolate and apple cider using the variables defined, we can use the following information:

• Let \( x \) be the number of hot chocolates sold, priced at $1 each.
• Let \( y \) be the number of apple ciders sold, priced at $2 each.

The total revenue generated from selling hot chocolate and apple cider can be represented with the equation:

\[ 1 \cdot x + 2 \cdot y \]

To ensure that the revenue is at least $250, we can create the following inequality:

\[ x + 2y \geq 250 \]

To write this inequality in standard form \( Ax + By \geq C \), we can rearrange it:

\[ -x - 2y \leq -250 \]

Thus, the standard form of the inequality representing the revenue generated by selling hot chocolate and apple cider is:

\[ x + 2y \geq 250 \]