To determine how many more chocolate bars Dennis needs to sell in order to win a prize, we can start by setting up an inequality based on the given information.
- Total needed to win a prize: Dennis needs to sell over $175 worth of chocolate.
- Current sales: He has already sold $40 worth of chocolate.
- Value of each chocolate bar: Each bar is sold for $2.50.
Let \( x \) represent the number of additional bars Dennis needs to sell. The total amount he will make from selling \( x \) bars is \( 2.50x \).
The total amount Dennis will have after selling \( x \) more bars is: \[ 40 + 2.50x \]
To win the prize, this total must be greater than $175: \[ 40 + 2.50x > 175 \]
Now, we will solve this inequality for \( x \):
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Subtract 40 from both sides: \[ 2.50x > 135 \]
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Divide both sides by 2.50: \[ x > \frac{135}{2.50} \]
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Calculate \( \frac{135}{2.50} \): \[ x > 54 \]
So, Dennis needs to sell more than 54 additional chocolate bars to win the prize. Since \( x \) must be a whole number, he needs to sell at least 55 more bars.
Therefore, the answer is: \[ x \geq 55 \]
This means that he needs to sell at least 55 more chocolate bars to qualify for the prize.
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