A metal fabricator starts with a single steel rod that measures exactly 4 yards and 2 feet… — Armed Services Vocational Aptitude Battery (ASVAB)

A metal fabricator starts with a single steel rod that measures exactly $4$ yards and $2$ feet in length. From this rod, they cut $7$ identical segments, each measuring exactly $1$ foot and $5$ inches long. Assuming no material is lost during the cutting process, how many inches of the steel rod remain?

Answer: 49 inches

Answer

49 inches

The correct answer is found by converting all lengths into inches (

4

yards

= 144

in,

2

feet

= 24

in, Total

= 168

in), finding the total length of the cut pieces (

7 \times 17

= 119

in), and subtracting the cuts from the total (

168 - 119 = 49

inches).

Step-by-Step Solution

Convert the total initial length of the steel rod into inches.

4

yards

= 144

inches;

2

feet

= 24

inches. Total

= 168

inches.

Converting to the smallest unit (inches) at the beginning prevents errors when subtracting later.

Convert the length of a single cut segment into inches.

1

foot

= 12

inches;

12 + 5 = 17

inches per segment.

The length of each cut segment must be in the same base unit as the total rod.

Calculate the total length of steel used for all

7

segments.

7 \times 17

inches

= 119

inches.

This determines the total amount of material that will be removed from the original rod.

Subtract the total used length from the initial rod length.

168

inches

- 119

inches

= 49

inches.

Subtracting the removed material from the starting material gives the final remaining length.

Key Concept

Converting multi-unit US Customary linear measurements to a common base unit to perform arithmetic operations.

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