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Difficulty: MediumDividing in a Ratio

A combat engineering detachment is mixing a specialized rapid-setting concrete. The dry mix requires sand, gravel, and cement in a ratio of 4:5:24:5:2 by weight. If the engineers need to prepare exactly 3,3003,300 pounds of the dry mix for a runway repair, how many pounds of gravel are required?

Answer: 1500 pounds

Answer

1500
To find the correct amount of gravel, the total weight of 3,3003,300 pounds is divided by the total number of parts in the ratio (4+5+2=114 + 5 + 2 = 11) to find the weight of one part (300300 pounds). The gravel's share is 5 parts, so multiplying 300300 pounds by 5 yields exactly 1,5001,500 pounds.

Step-by-Step Solution

1
Find the total number of parts in the ratio.
4+5+2=114 + 5 + 2 = 11 total parts
To distribute the total weight proportionally, you first need to know how many equal parts make up the entire mixture.
2
Determine the weight of one single part.
3,300÷11=3003,300 \div 11 = 300 pounds
Dividing the total weight of the mix by the total number of parts gives the value of one part.
3
Calculate the specific weight required for the gravel.
300×5=1,500300 \times 5 = 1,500 pounds
The ratio specifies 5 parts of gravel. Multiplying the weight of one part by 5 gives the total weight of the gravel.

Key Concept

Dividing a total quantity into given ratio parts.
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Topics

Dividing in a Ratio

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