A construction battalion is preparing a specialized concrete mix. The ratio of cement to s… — Armed Services Vocational Aptitude Battery (ASVAB)

A construction battalion is preparing a specialized concrete mix. The ratio of cement to sand by weight is $2:5$ , and the ratio of sand to gravel is $3:4$ . If the battalion needs to prepare exactly $3,280$ pounds of this concrete mix, how many pounds of gravel are required?

Answer: 1600 / 1,600 / 1600 pounds / 1,600 pounds / 1600 lbs / 1,600 lbs

Answer

1600 pounds

By converting the separate part-to-part ratios (

2:5

and

3:4

) into a single continuous ratio (

6:15:20

), we determine that gravel accounts for

20

out of the

41

total parts. Multiplying the total weight (

3,280

) by the fraction

\frac{20}{41}

yields exactly

1,600

pounds.

Step-by-Step Solution

Determine the combined continuous ratio of cement, sand, and gravel.

Cement:Sand:Gravel =

6:15:20

Since sand is the common element, find the least common multiple of its ratio shares (

5

and

3

), which is

15

. Multiply the first ratio by

3

and the second by

5

to align them.

Calculate the total number of parts in the combined ratio.

6 + 15 + 20 = 41

parts

To find the fraction of the total mix each part represents, all ratio parts must be summed.

Determine the weight of a single part.

3,280 \div 41 = 80

pounds per part

Divide the total weight by the total number of parts.

Calculate the total weight of the gravel.

20 \times 80 = 1,600

pounds

Multiply the weight of one part by the number of parts of gravel in the combined ratio.

Key Concept

Combined Ratios and Part-to-Whole Relationships

Alternative Method

You can also use algebra by setting the multiplier for the first ratio as

x

. Cement =

2x

and sand =

5x

. Since the ratio of sand to gravel is

3:4

, gravel must be

\frac{4}{3}

of sand, which is

\frac{20}{3}x

. The total is

2x + 5x + \frac{20}{3}x = \frac{41}{3}x = 3,280

. Solving for

x

gives

240

. Gravel is

\frac{20}{3}(240) = 1,600

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

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