Question

Cindy has $20 to spend at the store. She buys a pack of colored pencils that cost $4 and jelly beans that cost $2 per pound. If she spends more than $8 at the store, graph a compound inequality that shows the possible number of pounds of jelly beans she could have purchased.

Answer 1

Cindy can spend between $4 and $16 on jelly beans after buying colored pencils, leading to a compound inequality of 2 < p < 8, where p represents the pounds of jelly beans. This indicates she can buy more than 2 but less than 8 pounds.

Step-by-step explanation:

To graph a compound inequality representing the possible number of pounds of jelly beans Cindy could have purchased, we must first establish the total amount she can spend on them. We know Cindy has $20 to spend, and she spends $4 on colored pencils, leaving her with $16 for jelly beans. We also know she must spend more than $8 in total at the store, meaning she must spend more than $4 on jelly beans. Since jelly beans cost $2 per pound, we can write two inequalities to represent this scenario:

• 4 + 2p < 20
• 4 + 2p > 8

Now, solving each inequality for p (the number of pounds of jelly beans):

• 2p < 16, hence p < 8
• 2p > 4, hence p > 2

Combining these two inequalities gives us the compound inequality 2 < p < 8, which shows that Cindy can buy more than 2 pounds but less than 8 pounds of jelly beans.

To graph this compound inequality on a number line, we'd draw an open circle at 2 and an open circle at 8, with a line connecting the two, indicating all the numbers between 2 and 8 (but not including 2 and 8 themselves).