A civil engineering unit is mixing concrete for a rapid runway repair. The specialized mix… — Armed Services Vocational Aptitude Battery (ASVAB)

A civil engineering unit is mixing concrete for a rapid runway repair. The specialized mixture requires a weight ratio of $3$ parts Portland cement to $5$ parts aggregate. If a repair job requires a total of $400$ pounds of this dry mixture, how many pounds of Portland cement are needed?

A
$50$
$150$ Answer
C
$240$
D
$250$

Answer

The correct amount is

150

pounds.

The mixture consists of

3

parts cement and

5

parts aggregate, meaning there are

8

parts in total. Since the entire mixture weighs

400

pounds, each part weighs

50

pounds (

400 \div 8

). To find the amount of Portland cement, which represents

3

of those parts, we multiply

50

3

to get

150

pounds.

Step-by-Step Solution

Determine the total number of parts in the given ratio.

3 \text{ (cement)} + 5 \text{ (aggregate)} = 8 \text{ total parts}

Because the

400

pounds represents the entire mixture, we need to know the total parts that make up that whole mixture.

Calculate the weight of one single part.

400 \div 8 = 50 \text{ pounds per part}

Dividing the total weight by the total number of parts gives the value of a single proportional unit.

Calculate the total weight of the Portland cement.

50 \times 3 = 150 \text{ pounds}

The ratio specifies

3

parts of Portland cement, so we multiply the weight of one part by

3

Key Concept

Solving part-to-whole ratio problems by finding the sum of the ratio parts and determining the unit value of a single part.

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