Gary is using a 3D printer to create a miniature version of himself. The scale of the miniature is 0.4 inches to 1 foot oto Gary's actual height. If Gary is 5 feet and 9 inches tall, what will be the height of his 3D-Printed miniature? (12 inches=1 foot)

Options

A. 2.0 inches
B. 2.3 inches
C. 2.6 inches
D. 2.9 inches

Answer

To find the height of Gary's 3D-printed miniature, we can follow these steps:

### Step 1: Understand the scale
The scale of the miniature is given as 0.4 inches to 1 foot. This means for every 1 foot of Gary's height, the miniature will be 0.4 inches tall.

### Step 2: Convert Gary's height to inches
Gary's actual height is 5 feet and 9 inches. To convert this to inches:
- 1 foot = 12 inches
- Therefore, 5 feet = 5 × 12 = 60 inches
- Adding the extra 9 inches gives us:
\[ \text{Total height in inches} = 60 + 9 = 69 \text{ inches} \]

### Step 3: Set up the ratio
Let \( f \) be the height of the miniature and \( g \) be Gary's height. According to the scale:
\[ \frac{f}{g} = \frac{0.4 \text{ inches}}{1 \text{ foot}} = \frac{0.4 \text{ inches}}{12 \text{ inches}} = \frac{0.4}{12} \]
Thus, we can express this as:
\[ \frac{f}{69} = \frac{0.4}{12} \]

### Step 4: Solve for \( f \)
To find \( f \), we can rearrange the equation:
\[ f = 69 \times \frac{0.4}{12} \]

### Step 5: Simplify the calculation
Calculating \( \frac{0.4}{12} \):
\[ \frac{0.4}{12} = \frac{0.4 \div 4}{12 \div 4} = \frac{0.1}{3} \approx 0.0333 \]
Now substituting back:
\[ f = 69 \times 0.0333 \approx 2.3 \text{ inches} \]

### Final Answer
The height of Gary's 3D-printed miniature is approximately **2.3 inches**.