Question

Dennis has sold $40 worth of chocolate bars for a fundraiser. if he sells over $175 worth of chocolate, he'll win a prize. each bar is $2.50. how many more bars does he need to sell in order to win a prize
use inequality signs

Answer 1

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.

1. **Total needed to win a prize**: Dennis needs to sell over $175 worth of chocolate.
2. **Current sales**: He has already sold $40 worth of chocolate.
3. **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 \( x \):

1. Subtract 40 from both sides:
\[
2.50x > 135
\]

2. Divide both sides by 2.50:
\[
x > \frac{135}{2.50}
\]

3. 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.