Students at a local middle school are selling candy bars for a fund-raiser. The candy bars come packaged in cases of 60 bars, and the school makes a $0.75 profit from each candy bar sold. How many cases of candy bars need to be sold for the school to make a profit of $900?
20 cases of candy bars need to be sold for the school to make a profit of $900.
To determine the number of cases required to achieve a $900 profit, we first calculate the total profit from selling one case of candy bars. Each case contains 60 bars, and the school earns $0.75 per bar, leading to a profit of $45 per case. Dividing the target profit of $900 by $45 gives us 20 cases.
If 8 cases are sold, the total profit would amount to 8 cases × $45 per case = $360. This amount is significantly lower than the required profit of $900, indicating that more cases must be sold to reach the target.
Selling 12 cases yields a profit of 12 cases × $45 per case = $540. Although this profit is higher than selling 8 cases, it still falls short of the $900 goal, showing that further sales are necessary.
As previously calculated, selling 20 cases results in a profit of 20 cases × $45 per case = $900. This matches the desired profit exactly, making it the correct answer.
If 40 cases are sold, the profit calculates to 40 cases × $45 per case = $1,800. While this exceeds the target profit of $900, it is not the minimum number of cases required to achieve the goal, indicating an overestimation.
To achieve a profit of $900, the school must sell exactly 20 cases of candy bars, as this quantity precisely yields the necessary profit based on the earnings per case. Other choices either fall short of this target or exceed it without necessity, reinforcing that careful calculations based on profit per item are crucial in fundraising scenarios.
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