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Difficulty: EasyRatios, Rates, and Proportions

A contractor prepares a concrete mix using gravel and sand in a ratio of 4:74 : 7 by weight. If the contractor uses 2828 tons of sand for a project, what is the total weight, in tons, of the concrete mix?

  1. A
    1616
  2. B
    2121
  3. 4444Answer
  4. D
    4949
  5. E
    7777

Answer

The total weight of the concrete mix is 4444 tons.
The ratio of gravel to sand is 4:74 : 7. Sand corresponds to 77 parts of the total mixture and weighs 2828 tons, meaning 11 part represents 44 tons. The total mixture comprises 4+7=114 + 7 = 11 parts. Multiplying 1111 parts by 44 tons per part gives a total weight of 4444 tons.

Step-by-Step Solution

1
Determine the weight per ratio part using the known quantity of sand.
Since 77 parts equal 2828 tons of sand, 11 part =287=4= \frac{28}{7} = 4 tons.
The ratio specifies that sand accounts for 77 equal parts of the total mixture.
2
Calculate the weight of the gravel component.
Gravel weight =4 parts×4 tons/part=16= 4 \text{ parts} \times 4 \text{ tons/part} = 16 tons.
The ratio specifies that gravel accounts for 44 parts of the mixture.
3
Compute the total weight of the concrete mixture.
Total weight =16 tons (gravel)+28 tons (sand)=44= 16 \text{ tons (gravel)} + 28 \text{ tons (sand)} = 44 tons.
The total weight of the mixture is the sum of the weights of all individual ingredients.

Key Concept

Solving Proportions from Given Component Values
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Topics

Ratios, Rates, and Proportions

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