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Difficulty: EasyFractions, Decimals, and Percentages

A certain metal alloy is made of copper, zinc, and nickel. By weight, 14\frac{1}{4} of the alloy is copper, and 30%30\% of the alloy is zinc. What fraction of the alloy is nickel?

  1. A
    2120\frac{21}{20}
  2. B
    57\frac{5}{7}
  3. 920\frac{9}{20}Answer
  4. D
    12\frac{1}{2}
  5. E
    2140\frac{21}{40}

Answer

The fraction of the alloy that is nickel is 920\frac{9}{20}.
The correct answer is the fraction representing the remaining part of the alloy after accounting for copper and zinc. First, convert 30%30\% to the fraction 310\frac{3}{10}. The combined fraction of copper and zinc is 14+310=520+620=1120\frac{1}{4} + \frac{3}{10} = \frac{5}{20} + \frac{6}{20} = \frac{11}{20}. Subtracting this combined fraction from 11 yields the fraction of nickel: 1−1120=9201 - \frac{11}{20} = \frac{9}{20}.

Step-by-Step Solution

1
Convert the percentage of zinc to a fraction.
Since 30%=3010030\% = \frac{30}{100}, this simplifies to 310\frac{3}{10}.
To add or subtract the proportions of the alloy, they must be expressed in the same form (fractions).
2
Calculate the combined fraction of copper and zinc.
14+310=520+620=1120\frac{1}{4} + \frac{3}{10} = \frac{5}{20} + \frac{6}{20} = \frac{11}{20}.
To find how much of the alloy is made of copper and zinc combined, we add their individual fractions using a common denominator of 20.
3
Subtract the combined fraction from the whole to find the fraction of nickel.
1−1120=2020−1120=9201 - \frac{11}{20} = \frac{20}{20} - \frac{11}{20} = \frac{9}{20}.
Since the entire alloy represents a whole (11), the remaining portion must be nickel.

Key Concept

Expressing percentages as fractions and performing operations with fractions to solve part-to-whole problems.
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Topics

Fractions, Decimals, and Percentages

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