To find the actual length of the machine part based on the scale of the drawing, you will need to set up a proportion using the scale factor.
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First, convert the mixed number scale factor \( 15 \frac{1}{8} \) into an improper fraction: \[ 15 \frac{1}{8} = \frac{15 \times 8 + 1}{8} = \frac{120 + 1}{8} = \frac{121}{8} \]
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The length of the part in the drawing is \( 3 \frac{7}{8} \) inches. You will also convert this into an improper fraction: \[ 3 \frac{7}{8} = \frac{3 \times 8 + 7}{8} = \frac{24 + 7}{8} = \frac{31}{8} \]
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To find the actual length, let \( x \) be the actual length in inches. The scale factor relates the drawing length to the actual length: \[ \frac{\text{length in drawing}}{\text{actual length}} = \frac{1}{15 \frac{1}{8}} \] This can be written as: \[ \frac{\frac{31}{8}}{x} = \frac{1}{\frac{121}{8}} \]
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To solve for \( x \), cross-multiply: \[ \frac{31}{8} \cdot \frac{121}{8} = 1 \cdot x \] Which simplifies to: \[ x = \frac{31 \times 121}{8 \times 8} = \frac{3751}{64} \]
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Now, we can convert \( \frac{3751}{64} \) into a mixed number:
- Dividing \( 3751 \) by \( 64 \) gives approximately \( 58 \) remainder \( 43 \): \[ 3751 \div 64 = 58 \quad \text{(whole number)} \] \[ 3751 - (58 \times 64) = 3751 - 3712 = 39 \quad \text{(remainder)} \] So, \[ x = 58 \frac{39}{64} \]
The actual length of the machine part is approximately \( 58 \frac{39}{64} \) inches.
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