Let's solve Hank's problem step-by-step.
### Step 1: Understand the Ratio
Hank wants the ratio of the length to the width of the dog run to be 10.5:1.
### Step 2: Express the Ratio as an Equation
The ratio of length (L) to width (w) is given by:
[tex]\[ \frac{L}{w} = 10.5 \][/tex]
### Step 3: Isolate the Length (L)
We can rearrange the equation to express the length in terms of the width:
[tex]\[ L = 10.5 \times w \][/tex]
Therefore, the equation that can be used to solve for the width is:
[tex]\[ 10.5 \times w = L \][/tex]
### Step 4: Solve for Width (w)
To find the value of w, we can rearrange the equation to isolate w:
[tex]\[ w = \frac{L}{10.5} \][/tex]
Given that the length of the dog run is 10.5 feet, we can substitute this value into the equation:
[tex]\[ w = \frac{10.5}{10.5} \][/tex]
When we simplify this, we find:
[tex]\[ w = 1.0 \][/tex]
### Final Answers
1. The equation that can be used to solve for the width (w) is:
[tex]\[ 10.5 \times w = L \][/tex]
2. The value of [tex]\( w \)[/tex] is:
[tex]\[ 1.0 \][/tex]
So, the correct answers are:
- The equation that can be used to solve for the width (w) is: [tex]\( 10.5 \times w = L \)[/tex]
- The value of [tex]\( w \)[/tex] is: [tex]\( 1.0 \)[/tex]
