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At least how many grams of pure bronze must be alloyed with 387 grams of pure copper to create an alloy that is no more than 90% copper?
A. 13
B. 43
C. 103
D. 348
E. 430
A. 13
B. 43
C. 103
D. 348
E. 430
19 Jan 2017, 22:44
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Bunuel
At least how many grams of pure bronze must be alloyed with 387 grams of pure copper to create an alloy that is no more than 90% copper?
A. 13
B. 43
C. 103
D. 348
E. 430
A. 13
B. 43
C. 103
D. 348
E. 430
Hey,
PFB the solution.
Given:
- • Amount of pure copper = \(387\) grams.
Find:
- • Minimum amount of bronze in grams to be added, which results in copper less than or equal to \(90\)% in the alloy.
Approach and Working:
- • Let the amount of bronze added be \(x\) grams.
• Total amount will be the \((Copper + Bronze) = ( 387 + x)\) grams.
• Percentage of copper in the alloy \(= \frac{387}{(387 + x)}\) grams
• As per the given condition –
- o \(\frac{387}{(387+x)}\) ≤ \(\frac{90}{100}\)
o \(387*10\) ≤ \(9x + 387*9\)
o \(9x\) ≥ \(387\)
o \(x\) ≥ \(\frac{387}{9}\)
o \(x\) ≥ \(43\)
o Thus, the amount of bronze can be more than \(43\) grams, to ensure that percentage of copper is less than or equal to \(90\)% in the alloy.
• Butwe need to find the minimum amount of bronze needed, therefore, the least amount of bronze needed would be \(43\) grams.
• Correct Answer : Option B
Thanks,
Saquib
Quant Expert
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