Question
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In order to raise money to attend upcoming competitions, the debate team at Seaside High School is selling apple cider and hot chocolate at a basketball game. They hope to make at least $340 in revenue at tonight's game, with hot chocolate selling for $1 and hot apple cider selling for $2.
Select 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
Answers
GPT-4o mini
To formulate the inequality representing the situation, we need to take into account the prices of the drinks and the desired revenue.
Let:
- \( x \) = the number of hot chocolates sold (each sells for $1)
- \( y \) = the number of apple ciders sold (each sells for $2)
The total revenue from selling hot chocolate and apple cider can be expressed as:
- Revenue from hot chocolate: \( 1 \cdot x = x \)
- Revenue from hot apple cider: \( 2 \cdot y = 2y \)
Thus, the total revenue \( R \) can be expressed as:
\[ R = x + 2y \]
The team hopes to make at least $340 in revenue, which gives us the inequality:
\[ x + 2y \geq 340 \]
Now, we write this in standard form, which typically means rearranging it to have all variables on one side and the constant on the other side.
The standard form of the inequality will therefore be:
\[ x + 2y - 340 \geq 0 \]
This standard form representation indicates that, to achieve their goal, the combined revenue from selling hot chocolate and apple cider must be at least $340.
So, the final inequality in standard form is:
\[ x + 2y \geq 340 \]
Let:
- \( x \) = the number of hot chocolates sold (each sells for $1)
- \( y \) = the number of apple ciders sold (each sells for $2)
The total revenue from selling hot chocolate and apple cider can be expressed as:
- Revenue from hot chocolate: \( 1 \cdot x = x \)
- Revenue from hot apple cider: \( 2 \cdot y = 2y \)
Thus, the total revenue \( R \) can be expressed as:
\[ R = x + 2y \]
The team hopes to make at least $340 in revenue, which gives us the inequality:
\[ x + 2y \geq 340 \]
Now, we write this in standard form, which typically means rearranging it to have all variables on one side and the constant on the other side.
The standard form of the inequality will therefore be:
\[ x + 2y - 340 \geq 0 \]
This standard form representation indicates that, to achieve their goal, the combined revenue from selling hot chocolate and apple cider must be at least $340.
So, the final inequality in standard form is:
\[ x + 2y \geq 340 \]