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Question

Difficulty: MediumRatios, Rates, and Proportions

A chef prepares a spice mix by combining paprika, cumin, and coriander in a ratio of 8:5:28 : 5 : 2 by weight. If the chef wants to make a total of 6060 ounces of the spice mix, how many ounces of cumin are needed?

  1. A
    15
  2. 20Answer
  3. C
    30
  4. D
    37.5

Answer

The correct answer is 20 ounces.
The correct answer is 20 ounces. To find the amount of cumin needed, first sum the parts of the ratio to find the total parts of the mixture: 8+5+2=158 + 5 + 2 = 15 parts. Since cumin represents 5 of these 15 parts, the fraction of the spice mix that is cumin is 515\frac{5}{15}, which simplifies to 13\frac{1}{3}. Multiplying this fraction by the total desired weight of the spice mix gives 13×60=20\frac{1}{3} \times 60 = 20 ounces.

Step-by-Step Solution

1
Calculate the total number of parts in the ratio.
8+5+2=158 + 5 + 2 = 15 parts.
Determining the total parts is necessary to find what fraction of the whole mixture is represented by cumin.
2
Determine the fractional portion of the mixture that is cumin.
The fraction is 515\frac{5}{15}, which simplifies to 13\frac{1}{3}.
This fraction represents the ratio of the cumin parts to the total parts of the spice mix.
3
Multiply the cumin fraction by the total weight of the mix to find the weight of cumin.
13×60=20\frac{1}{3} \times 60 = 20 ounces.
Multiplying the proportion of cumin by the total desired weight of the spice mix yields the required ounces of cumin.

Key Concept

Solving part-to-whole ratio problems by finding the total number of parts and applying the fraction to the overall amount.
Estimated Time:1m 15s
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Topics

Ratios, Rates, and Proportions

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