A certain metal alloy is made of copper, zinc, and nickel. By weight, \frac{1}{4} of the a… — ACT

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

A
$\frac{21}{20}$
B
$\frac{5}{7}$
$\frac{9}{20}$ Cevap
D
$\frac{1}{2}$
E
$\frac{21}{40}$

Cevap

The fraction of the alloy that is nickel is

\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\%

to the fraction

\frac{3}{10}

. The combined fraction of copper and zinc is

\frac{1}{4} + \frac{3}{10} = \frac{5}{20} + \frac{6}{20} = \frac{11}{20}

. Subtracting this combined fraction from

1

yields the fraction of nickel:

1 - \frac{11}{20} = \frac{9}{20}

Adım Adım Çözüm

Convert the percentage of zinc to a fraction.

Since

30\% = \frac{30}{100}

, this simplifies to

\frac{3}{10}

To add or subtract the proportions of the alloy, they must be expressed in the same form (fractions).

Calculate the combined fraction of copper and zinc.

\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.

Subtract the combined fraction from the whole to find the fraction of nickel.

1 - \frac{11}{20} = \frac{20}{20} - \frac{11}{20} = \frac{9}{20}

Since the entire alloy represents a whole (

1

), the remaining portion must be nickel.

Anahtar Kavram

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

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Adım Adım Çözüm

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