Question

question 12 of 23 - multiple choice

four pieces of wood, each 38-1/2\ long, will be cut from one long piece of stock. if the waste due to each saw kerf is 1/8\, what is the minimal length of wood needed?

a 12 9-3/8\
b 12 9\
c 12 10-3/8\
d 12 9-7/8\

Explanation:

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<reasoning>

Calculate total length of wood pieces

Using the Fraction Arithmetic and Fraction Word Problems knowledge points
\[
L_{\text{pieces}} = 4 \times 38\frac{1}{2}'' = 4 \times 38.5'' = 154''
\]

Calculate total saw kerf waste

Using the Construction Math knowledge point
\[

$$\begin{aligned} N_{\text{cuts}} &= 4 - 1 = 3 \\ W_{\text{total}} &= 3 \times \frac{1}{8}'' = \frac{3}{8}'' \end{aligned}$$

\]

Calculate total minimal length in inches

Using the Fraction Arithmetic knowledge point
\[
L_{\text{total}} = 154'' + \frac{3}{8}'' = 154\frac{3}{8}''
\]

Convert total length to feet and inches

Using the Construction Math knowledge point
\[

$$\begin{aligned} 154'' \div 12 &= 12 \text{ ft with a remainder of } 10'' \\ L_{\text{total}} &= 12' \text{ } 10\frac{3}{8}'' \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>A) 12' 9-3/8"</mcq-option>
<mcq-option>B) 12' 9"</mcq-option>
<mcq-correct>C) 12' 10-3/8"</mcq-correct>
<mcq-option>D) 12' 9-7/8"</mcq-option>
</answer>

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Answer:

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<reasoning>

Calculate total length of wood pieces

Using the Fraction Arithmetic and Fraction Word Problems knowledge points
\[
L_{\text{pieces}} = 4 \times 38\frac{1}{2}'' = 4 \times 38.5'' = 154''
\]

Calculate total saw kerf waste

Using the Construction Math knowledge point
\[

$$\begin{aligned} N_{\text{cuts}} &= 4 - 1 = 3 \\ W_{\text{total}} &= 3 \times \frac{1}{8}'' = \frac{3}{8}'' \end{aligned}$$

\]

Calculate total minimal length in inches

Using the Fraction Arithmetic knowledge point
\[
L_{\text{total}} = 154'' + \frac{3}{8}'' = 154\frac{3}{8}''
\]

Convert total length to feet and inches

Using the Construction Math knowledge point
\[

$$\begin{aligned} 154'' \div 12 &= 12 \text{ ft with a remainder of } 10'' \\ L_{\text{total}} &= 12' \text{ } 10\frac{3}{8}'' \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>A) 12' 9-3/8"</mcq-option>
<mcq-option>B) 12' 9"</mcq-option>
<mcq-correct>C) 12' 10-3/8"</mcq-correct>
<mcq-option>D) 12' 9-7/8"</mcq-option>
</answer>

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