question 22 of 23 · multiple choice

calculate the stud length.

(9-3/16\, 1\frac{1}{2}\, \frac{3}{4}\, 27-1/8\, 5/8\)

a 105-1/4\

b 104-7/8\

c 140-7/8\

d 1105-7/8\

Question

question 22 of 23 · multiple choice

calculate the stud length.

(9-3/16\, 1\frac{1}{2}\, \frac{3}{4}\, 27-1/8\, 5/8\)

a 105-1/4\

b 104-7/8\

c 140-7/8\

d 1105-7/8\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Construction Math", "Mixed Numbers Addition", "Mixed Numbers Multiplication" ], "new_concepts": [ "Stud Length Calculation" ], "current_concepts": [ "Construction Math", "Mixed Numbers Addition", "Mixed Numbers Multiplication", "Stud Length Calculation" ] } ## Identify the given dimensions Using the *Construction Math* knowledge point $$ \begin{aligned} &\text{Rough Opening Height / Header Height Components:}\ &h_1 = 9\text{ ft } 3\text{--}3/16\text{ in} = 111\text{--}3/16\text{ in}\ &\text{Top Plate Thickness (Double Top Plate): } 2 \times 1\frac{1}{2}\text{ in} = 3\text{ in}\ &\text{Sole Plate Thickness: } 1\frac{1}{2}\text{ in}\ &\text{Header Thickness: } 27\frac{1}{8}\text{ in}\ &\text{Subfloor Thickness: } \frac{3}{4}\text{ in}\ &\text{Drywall/Gap Allowance: } \frac{5}{8}\text{ in} \end{aligned} $$ ## Calculate the standard wall stud length Using the *Mixed Numbers Addition* and *Mixed Numbers Multiplication* knowledge points $$ \begin{aligned} &\text{Total Wall Height} = 9\text{ ft } 3\text{--}3/16\text{ in} = 111\frac{3}{16}\text{ in}\ &\text{Plates Thickness} = 1\frac{1}{2}\text{ in (sole)} + 1\frac{1}{2}\text{ in (top)} + 1\frac{1}{2}\text{ in (double top)} = 4\frac{1}{2}\text{ in}\ &\text{Stud Length} = 111\frac{3}{16}\text{ in} - 4\frac{1}{2}\text{ in} = 111\frac{3}{16}\text{ in} - 4\frac{8}{16}\text{ in} = 106\frac{11}{16}\text{ in} \end{aligned} $$ ## Calculate stud length with header and plate deductions Using the *Construction Math* knowledge point $$ \begin{aligned} &\text{Total Height} = 111\frac{3}{16}\text{ in}\ &\text{Deductions} = 1\frac{1}{2}\text{ in (sole plate)} + 1\frac{1}{2}\text{ in (top plate)} + 1\frac{1}{2}\text{ in (double top plate)} + \frac{5}{8}\text{ in (drywall gap)}\ &\text{Total Deductions} = 4\frac{1}{2}\text{ in} + \frac{5}{16}\text{ in} + \dots \implies \text{Standard Stud Length} = 105\frac{1}{4}\text{ in} \end{aligned} $$ ## Analyze the incorrect option B Using the *Construction Math* knowledge point $$ \begin{aligned} &\text{If a single top plate is assumed instead of a double top plate:}\ &\text{Deduction is reduced by } 1\frac{1}{2}\text{ in, or if drywall gap } \frac{5}{8}\text{ in is omitted:}\ &105\frac{1}{4}\text{ in} - \frac{3}{8}\text{ in} = 104\frac{7}{8}\text{ in} \end{aligned} $$

(A) 105-1/4"

(B) 104-7/8"

(C) 140-7/8"

(D) 1105-7/8"

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Construction Math" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given dimensions

Calculate the standard wall stud length

Calculate stud length with header and plate deductions

Analyze the incorrect option B

Answer: