A cabinetmaker uses the standard pennyweight formula, \text{Length} = \frac{d}{4} + 0.5\te… — Armed Services Vocational Aptitude Battery (ASVAB)

A cabinetmaker uses the standard pennyweight formula, $\text{Length} = \frac{d}{4} + 0.5\text{ inches}$ , to determine fastener dimensions for sizes up to $10\text{d}$ , where $d$ represents the penny size number. What is the total length, in inches, of a $4\text{d}$ nail?

Answer: 1.5 inches

Answer

The total length of a

4\text{d}

nail is

1.5\text{ inches}

Using the standard carpentry formula for nails between

2\text{d}

and

10\text{d}

(

\text{Length} = \frac{d}{4} + 0.5\text{ inches}

), substituting

d = 4

yields

\frac{4}{4} + 0.5 = 1 + 0.5 = 1.5\text{ inches}

Step-by-Step Solution

Identify the variable

d

representing the penny rating.

d = 4

The question specifies a

4\text{d}

nail.

Substitute

d = 4

into the nail length formula

\text{Length} = \frac{d}{4} + 0.5

\text{Length} = \frac{4}{4} + 0.5

The standard empirical formula relates penny size to physical inch length.

Perform arithmetic evaluation to find the final length.

1.5\text{ inches}

Dividing

4

4

gives

1

, and adding

0.5

yields

1.5

Key Concept

Nail Pennyweight (d) Sizing System

Estimated Time:45s

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