Question

lucias family likes to have bagels for breakfast. at the bakery, lucia orders 20 bagels. she wants fewer than 12 of them to be blueberry bagels and the rest to be cinnamon raisin bagels.
let b represent the number of blueberry bagels lucia might get. which inequality models the story?
$b > 12$ $b > 20$ $b < 12$ $b < 20$
graph the inequality that models the story.
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.
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Explanation:

Step1: Analyze the problem

Lucia orders 20 bagels, and she wants fewer than 12 of them to be blueberry bagels. Let \( b \) be the number of blueberry bagels. So we need to find the inequality that represents \( b \) being less than 12.

Step2: Evaluate the options

• Option \( b>12 \): This would mean more than 12 blueberry bagels, which is not what we want.
• Option \( b > 20 \): Since she only ordered 20 bagels, the number of blueberry bagels can't be more than 20, but this is not the main condition here.
• Option \( b<12 \): This represents the number of blueberry bagels being fewer than 12, which matches the problem statement.
• Option \( b < 20 \): While it's true that the number of blueberry bagels can't exceed 20, the key condition is that it's fewer than 12, so this is not the correct inequality for the story.

For graphing \( b < 12 \):

• The endpoint is at 12, and since \( b \) is strictly less than 12, the endpoint is open (not filled).
• The arrow points to the left (towards smaller numbers) because we want values of \( b \) less than 12. So we plot an open circle at 12 and draw a ray to the left.

Answer:

The inequality is \( \boldsymbol{b < 12} \). For the graph, plot an open circle at 12 on the number line and draw a ray pointing to the left (towards numbers less than 12).