Question

Problem situation: bernie spends $6.50 on ingredients and cups for his lemonade stand. he charges $1.50 for each cup of lemonade. he will only sell whole cups of lemonade (not 0.75 cups, 1.5 cups, etc.). how many cups, x , will bernie need to sell to make a profit of at least $20 ? inequality that represents this situation: 20≤1.50x−6.50 drag each number to show if it is a solution to both the inequality and the problem situation or to the inequality only, or if it is not a solution.

Answer 1

To make at least a $20 profit, Bernie needs to sell a minimum of 18 cups of lemonade, as selling 17 cups would not meet the required profit threshold.

Step-by-step explanation:

The student is asking how many cups of lemonade Bernie needs to sell to make a profit of at least $20. The inequality that represents Bernie's situation is 20 ≤ 1.50x - 6.50, where x is the number of cups sold. To find the number of cups Bernie must sell to break even and then make a $20 profit, we must solve for x in the inequality.

First, add $6.50 to both sides of the inequality to isolate the term involving x on one side:

20 + 6.50 ≤ 1.50x

26.50 ≤ 1.50x

Next, divide both sides by $1.50 to solve for x:

26.50 / 1.50 ≤ x

x ≥ 17.67

Since Bernie can only sell whole cups of lemonade, he must sell at least 18 cups to make a minimum of $20 in profit. Selling 18 cups will bring in $27 ($1.50 × 18), which after deducting the initial investment of $6.50, results in a profit of $20.50.

Answer 2

Bernie needs to sell at least 18 whole cups of lemonade to make a profit of at least $20, as per the inequality 20≤ 1.50x - 6.50.

Step-by-step explanation:

To determine how many cups of lemonade Bernie needs to sell to make a profit of at least $20, we can use the given inequality 20≤ 1.50x - 6.50, where x represents the number of cups sold. We start by adding $6.50 to both sides of the inequality to isolate the term involving x on one side, resulting in 26.50 ≤ 1.50x.

Next, we divide both sides of the inequality by $1.50 to solve for x, yielding x ≥ 17.67. Because Bernie sells only whole cups, he must sell at least 18 cups to make the desired profit.