Question

a sports club needs to raise at least $500 by selling chocolate bars for $2.50 each. sebastian wants to know how many chocolate bars, c, the sports club must sell in order to reach its goal. which of the following must be true about the inequality and the resulting graph? select three options. the inequality should be written as 2.50c ≥ 500. the inequality should be written as 2.50c ≤ 500. the circle is open. the circle is closed. the arrow points right.

Explanation:

Step1: Formulate the inequality

Since each chocolate bar is sold for $2.50 and the club needs to raise at least $500, the inequality is \(2.50c\geq500\).

Step2: Analyze the inequality symbol for the graph

The symbol \(\geq\) means that the value \(c\) can be equal to the solution. So, on the number - line graph, the circle is closed.

Step3: Determine the direction of the arrow

When solving \(2.50c\geq500\) for \(c\) (divide both sides by \(2.50\), \(c\geq\frac{500}{2.50}=200\)), values of \(c\) that are greater than or equal to 200 are solutions. So, the arrow points to the right.

Answer:

The inequality should be written as \(2.50c\geq500\), the circle is closed, the arrow points right. So the correct options are:

• The inequality should be written as \(2.50c\geq500\)
• The circle is closed
• The arrow points right