A naval shipyard receives a shipment of 945 tons of specialized steel plating. The shipyar… — Armed Services Vocational Aptitude Battery (ASVAB)

A naval shipyard receives a shipment of $945$ tons of specialized steel plating. The shipyard superintendent allocates $\frac{4}{9}$ of this shipment specifically for submarine hull repairs. If each submarine repair module requires exactly $17 \frac{1}{2}$ tons of steel plating, how many complete repair modules can be outfitted from the allocated steel?

Answer: 24 modules

Answer

The correct answer is found by first calculating the portion of the steel available for repairs (

945 \times \frac{4}{9} = 420

tons), and then dividing that available amount by the requirement per module (

420 \div 17 \frac{1}{2} = 420 \times \frac{2}{35} = 24

complete modules).

Step-by-Step Solution

Determine the total amount of steel allocated for submarine repairs.

420 tons

The problem states that only

\frac{4}{9}

of the

945

ton shipment is allocated for this specific purpose, requiring multiplication:

945 \times \frac{4}{9} = 105 \times 4 = 420

Convert the mixed number representing the steel required per module into an improper fraction.

\frac{35}{2}

tons

Converting

17 \frac{1}{2}

to an improper fraction (

\frac{17 \times 2 + 1}{2} = \frac{35}{2}

) is necessary to accurately divide the total allocated steel.

Calculate the number of complete modules by dividing the allocated steel by the required steel per module.

24 modules

Dividing the total allocated amount (

420

tons) by the amount needed per module (

\frac{35}{2}

tons) gives the number of modules:

420 \div \frac{35}{2} = 420 \times \frac{2}{35} = 12 \times 2 = 24

Key Concept

Applying fraction multiplication to find a portion of a whole, followed by fraction division to determine how many equal groups can be formed.

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