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Difficulty: MediumRatios, Rates, and Proportions

A commercial bakery makes a specialty flour blend using whole wheat flour, rye flour, and white flour in a ratio of 3:2:53 : 2 : 5 by weight, respectively. To prepare a batch for a large order, a baker uses 36 pounds36\text{ pounds} of whole wheat flour. If rye flour costs $1.50\$1.50 per pound and white flour costs $0.80\$0.80 per pound, what is the total cost of the rye flour and white flour needed for this batch?

  1. A
    $25.20\$25.20
  2. B
    $73.20\$73.20
  3. $84.00\$84.00Answer
  4. D
    $109.20\$109.20
  5. E
    $120.00\$120.00

Answer

The total cost of the rye flour and white flour needed for this batch is $84.00\$84.00.
To find the cost, first determine the weight per ratio part. Whole wheat represents 33 parts out of 3:2:53 : 2 : 5, so 33 parts equal 36 pounds36\text{ pounds}, making 1 part=12 pounds1\text{ part} = 12\text{ pounds}. Thus, the batch requires 2×12=24 pounds2 \times 12 = 24\text{ pounds} of rye flour and 5×12=60 pounds5 \times 12 = 60\text{ pounds} of white flour. At $1.50\$1.50 per pound, the rye flour costs 24×$1.50=$36.0024 \times \$1.50 = \$36.00. At $0.80\$0.80 per pound, the white flour costs 60×$0.80=$48.0060 \times \$0.80 = \$48.00. Adding these together gives a total cost of $36.00+$48.00=$84.00\$36.00 + \$48.00 = \$84.00.

Step-by-Step Solution

1
Determine the weight represented by one ratio part
Since whole wheat flour represents 33 parts of the ratio and equals 36 pounds36\text{ pounds}, 1 part=363=12 pounds1\text{ part} = \frac{36}{3} = 12\text{ pounds}.
Dividing the known quantity by its corresponding ratio weight finds the unit multiplier for the proportional relationship.
2
Calculate the weight of rye flour and white flour needed
Rye flour (22 parts) =2×12=24 pounds= 2 \times 12 = 24\text{ pounds}. White flour (55 parts) =5×12=60 pounds= 5 \times 12 = 60\text{ pounds}.
Multiply each component's ratio value by the single-part weight value.
3
Calculate the cost of each ingredient and sum them
Cost of rye flour =24×$1.50=$36.00= 24 \times \$1.50 = \$36.00. Cost of white flour =60×$0.80=$48.00= 60 \times \$0.80 = \$48.00. Total cost =$36.00+$48.00=$84.00= \$36.00 + \$48.00 = \$84.00.
Multiply the weight of each ingredient by its unit price and add the totals together.

Key Concept

Solving multi-part ratio problems by finding a common multiplier and using unit rates.
Estimated Time:1m 15s
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Topics

Ratios, Rates, and Proportions

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