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  • In two different nickel alloys, there was 6 kg nickel in the first alloy and 12 kg in the second alloy. The percentage of nickel in the first alloy was 40 percentage points less than the percentage

In two different nickel alloys, there was 6 kg nickel in the first alloy and 12 kg in the second alloy. The percentage of nickel in the first alloy was 40 percentage points less than the percentage of nickel in the second alloy. After melting these two alloys together the resulting alloy contained 36 percent of nickel. What was the percentage of nickel in the first and the second alloy?

Answers (1)

best_answer

Given:

Nickel in first alloy = 6 kg
Nickel in second alloy = 12 kg
Percentage of nickel in the first alloy is 40 percentage points less than in the second
Final alloy has 36% nickel
 

Let the percentage of nickel in the second alloy be \( x\%\).  
Then the percentage of nickel in the first alloy is \( (x - 40)\%\).

Let the mass of the first alloy be \( A \) and the mass of the second alloy be \( B \).

{From the given:}
\[
\frac{x - 40}{100} \cdot A = 6 \tag{1}
\]
\[
\frac{x}{100} \cdot B = 12 \tag{2}
\]

{Total mass of final alloy:}
\[
A + B = \frac{18}{0.36} = 50 \tag{3}
\]

{From equations (1) and (2):}
\[
A = \frac{600}{x - 40}, \quad B = \frac{1200}{x}
\]

Substitute into (3):
\[
\frac{600}{x - 40} + \frac{1200}{x} = 50
\]

Multiply through by \( x(x - 40) \):
\[
600x + 1200(x - 40) = 50x(x - 40)
\]

Simplify:
\[
600x + 1200x - 48000 = 50x^2 - 2000x
\]
\[
1800x - 48000 = 50x^2 - 2000x
\]
\[
0 = 50x^2 - 3800x + 48000
\]

Divide by 10:
\[
5x^2 - 380x + 4800 = 0
\]

Solve using quadratic formula:
\[
x = \frac{380 \pm \sqrt{(-380)^2 - 4 \cdot 5 \cdot 4800}}{2 \cdot 5}
= \frac{380 \pm \sqrt{144400 - 96000}}{10}
= \frac{380 \pm \sqrt{48400}}{10}
\]
\[
\sqrt{48400} = 220 \Rightarrow x = \frac{380 \pm 220}{10}
\]

So, the possible values are:
\[
x = \frac{600}{10} = 60, \quad x = \frac{160}{10} = 16
\]

Only \( x = 60 \) is valid (as \( x = 16 \Rightarrow \) first alloy = -24\%, not possible)

{Final Answer:}
\[
\text{Percentage of nickel in first alloy} = 60 - 40 = \boxed{20\%}
\]
\[
\text{Percentage of nickel in second alloy} = \boxed{60\%}
\]


 

Posted by

Saumya Singh

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