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Difficulty: MediumDividing in a Ratio

A construction crew is pouring a foundation that requires 3.63.6 tons of a custom gravel and sand mixture. If the mixture contains gravel and sand in a ratio of 5:45:4, how many pounds of sand are required for the foundation? (11 ton =2,000= 2,000 pounds)

  1. A
    1,6001,600
  2. B
    5,7605,760
  3. 3,2003,200Answer
  4. D
    4,0004,000

Answer

The required amount of sand is 3,2003,200 pounds.
The correct answer is found by first converting the total weight to pounds (3.6×2,000=7,2003.6 \times 2,000 = 7,200 pounds). The total number of parts in the ratio is 5+4=95 + 4 = 9. Dividing the total weight by the total parts gives the weight of one part (7,200÷9=8007,200 \div 9 = 800 pounds). Since the sand is the second component of the 5:45:4 ratio, it represents 44 parts. Multiplying the weight of one part by 44 gives 3,2003,200 pounds.

Step-by-Step Solution

1
Convert the total weight of the mixture from tons to pounds.
3.6 tons×2,000 pounds/ton=7,200 pounds3.6 \text{ tons} \times 2,000 \text{ pounds/ton} = 7,200 \text{ pounds}
The question asks for the final answer in pounds, so it is necessary to standardize the units first.
2
Determine the total number of parts in the ratio.
5+4=9 total parts5 + 4 = 9 \text{ total parts}
To find the value of a single part, you must know how many equal parts make up the whole mixture.
3
Calculate the weight of one ratio part.
7,200 pounds÷9 parts=800 pounds/part7,200 \text{ pounds} \div 9 \text{ parts} = 800 \text{ pounds/part}
Dividing the total weight by the total number of parts gives the weight of one proportional unit.
4
Calculate the total weight of the sand.
4 parts×800 pounds/part=3,200 pounds4 \text{ parts} \times 800 \text{ pounds/part} = 3,200 \text{ pounds}
The ratio of gravel to sand is 5:45:4, meaning the sand accounts for exactly 44 of the 99 total parts.

Key Concept

Dividing in a Ratio
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Topics

Dividing in a Ratio

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