Question

Use the drawing tool(s) to form the correct answer on the provided number line.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

We are given the following information.

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.

Let x be the number of pounds of jelly beans.

With the above information, we can set up the following inequality

`4+2x\leq20`

Less than or equal to sign is used because Cindy can only spend equal to or less than $20.

We are also given that she spends more than $8 at the store.

We can set up the following inequality

`4+2x>8`

Now, let us solve these two inequalities one by one.

`\begin{gathered} 4+2x\leq20 \\ 2x\leq20-4 \\ 2x\leq16 \\ (2x)/(2)\leq(16)/(2) \\ x\leq8 \end{gathered}`
`\begin{gathered} 4+2x>8 \\ 2x>8-4 \\ 2x>4 \\ (2x)/(2)>(4)/(2) \\ x>2 \end{gathered}`

So, the compound inequality is

[tex]2The above compound inequality means that the number of pounds of jelly beans Cindy can purchase is greater than 2 and equal to or less than 8.

Finally, let us graph the inequality on the number line.

Use an open point at 2 and a closed point at 8.