Examkin

Question

Difficulty: MediumRatios, Rates, and Proportions

A jeweler creates a custom alloy by melting gold, silver, and copper in a ratio of 9:4:29:4:2 by weight, respectively. If the jeweler uses 1212 ounces of silver to make the alloy, what is the total weight, in ounces, of the alloy produced?

  1. A
    20
  2. B
    27
  3. C
    33
  4. 45Answer
  5. E
    90

Answer

The correct answer is 45 ounces.
The correct answer is 45. In the gold, silver, and copper ratio of 9:4:29:4:2, silver represents 44 parts. Since the jeweler uses 1212 ounces of silver, each part is equal to 12÷4=312 \div 4 = 3 ounces. The total weight consists of 9+4+2=159 + 4 + 2 = 15 parts. Multiplying the total parts by the weight of each part gives 15×3=4515 \times 3 = 45 ounces.

Step-by-Step Solution

1
Determine the value of one part in the ratio based on the given weight of silver.
Since silver corresponds to 4 parts in the 9:4:29:4:2 ratio, we set up 4x=124x = 12, which gives x=3x = 3 ounces per part.
Finding the unit rate per part allows us to scale up to the total parts.
2
Find the total number of parts in the alloy.
Total parts = 9+4+2=159 + 4 + 2 = 15 parts.
The total weight of the alloy is represented by the sum of the ratio parts of all components.
3
Calculate the total weight by multiplying the total parts by the weight per part.
Total weight = 15×3=4515 \times 3 = 45 ounces.
This yields the complete weight of the gold, silver, and copper combined.

Key Concept

Solving multi-part ratio word problems by finding the unit value of a single part and scaling it to find the total amount.
Estimated Time:1m 0s
Rate this question

Topics

Ratios, Rates, and Proportions

More questions from this topic