Let's break down the problem step by step to find an inequality that represents the number of days Darcie can skip and still meet her goal.
### Step 1: Understand the Problem
Darcie wants to crochet a total of 3 blankets, and she crochets [tex]$\frac{1}{15}$[/tex] of a blanket per day. She has a total of 60 days to complete this task but also wants to know how many days she can skip crocheting.
### Step 2: Calculate the Total Number of Days Needed
First, we calculate how many days Darcie needs to crochet to make 3 blankets:
[tex]\[ \text{Days needed} = \frac{\text{Blankets required}}{\text{Rate per day}} = \frac{3}{\frac{1}{15}} \][/tex]
[tex]\[ \text{Days needed} = 3 \times 15 = 45 \][/tex]
Darcie needs 45 days to crochet the 3 blankets.
### Step 3: Determine the Inequality for the Days Darcie Can Skip
Darcie has a total of 60 days. Let [tex]\( s \)[/tex] be the number of days she can skip. Therefore, the sum of the number of days needed to crochet and the days she skips should be less than or equal to the total days:
[tex]\[ \text{Days needed} + s \leq 60 \][/tex]
[tex]\[ 45 + s \leq 60 \][/tex]
Subtracting 45 from both sides gives:
[tex]\[ s \leq 15 \][/tex]
Thus, the inequality that represents the number of days Darcie can skip is:
[tex]\[ s \leq 15 \][/tex]
### Step 4: Graph the Inequality
To graph the inequality [tex]\( s \leq 15 \)[/tex], follow these steps:
1. Draw a number line representing possible values for [tex]\( s \)[/tex].
2. Mark the point 15 on the number line.
3. Shade all the points to the left of 15, including 15, because Darcie can skip any number of days up to and including 15 days.
Here is a simple representation of the graph:
[tex]\[
\begin{array}{rl}
\cdots & \leftarrow \text{ continue this pattern }
\\
0 & \bullet \ ← 0 (Days skipped)
\\
1 & \bullet
\\
2 & \bullet
\\
\cdots & \leftarrow \text{ continue marking }
\\
14 & \bullet
\\
15 & \bullet \standardLimits {\leftarrow \text{ 15 (Maximum days skipped)}
\\
16 & \circ \standardLimits {\leftarrow \text{ 16 (Cannot skip more than 15 days)}
\\
\cdots & \leftarrow \text{ continue this pattern }
\end{array}
\][/tex]
To summarize:
- Darcie can skip up to 15 days and still meet her goal.
- The inequality representing the number of days Darcie can skip is [tex]\( s \leq 15 \)[/tex].
