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100 kgs of an alloy of tin and lead in the ratio 1:3 is mixed with x k 15 Apr 2020, 05:47
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100 kgs of an alloy of tin and lead in the ratio 1:3 is mixed with x kgs of an alloy of tin and lead in the ratio 3:2. If the overall alloy should contain between 40% and 50% tin, what is the range of values x can take?

A. 100 kgs ≤ x ≤ 200 kgs
B. 110 kgs ≤ x ≤ 240 kgs
C. 105 kgs ≤ x ≤ 220 kgs
D. 75 kgs ≤ x ≤ 250 kgs
E. 60 kgs ≤ x ≤ 150 kgs


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D
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nick1816
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100 kgs of an alloy of tin and lead in the ratio 1:3 is mixed with x k 15 Apr 2020, 09:05
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% of tin in first alloy = 25

% of tin in second alloy = 60

25............60
........40.......
x................y

y/x = 15/20 = 75/100


25............60
........50.......
x................y

y/x = 25/10 = 250/100

D


Bunuel
100 kgs of an alloy of tin and lead in the ratio 1:3 is mixed with x kgs of an alloy of tin and lead in the ratio 3:2. If the overall alloy should contain between 40% and 50% tin, what is the range of values x can take?

A. 100 kgs ≤ x ≤ 200 kgs
B. 110 kgs ≤ x ≤ 240 kgs
C. 105 kgs ≤ x ≤ 220 kgs
D. 75 kgs ≤ x ≤ 250 kgs
E. 60 kgs ≤ x ≤ 150 kgs


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100 kgs of an alloy of tin and lead in the ratio 1:3 is mixed with x k 15 Apr 2020, 09:14
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100 kgs of an alloy of tin and lead in the ratio 1:3 is mixed with x kgs of an alloy of tin and lead in the ratio 3:2. If the overall alloy should contain between 40% and 50% tin, what is the range of values x can take?

First 100kg, at a ratio of 1:3 tin and lead contains 25kg tin. (100kg * 1/4)
Next x kg contain 3:2 ratio of tin and lead. Therefore it is 60% (3/5) tin.

Minimum value of X (for 40% tin overall) :
25+0.6X/100+X = 0.4
(*100+X)
25+0.6X=40+0.4X
0.6X=15+0.4X
0.2X=15
X=75

Maximum value of X (for 50% tin overall):
25+0.6X/100+X = 0.5
(*100+X)
25+0.6X=50+0.5X
0.6X=25+0.5X
0.1X=25
X=250

Therefore 75 kgs ≤ x ≤ 250 kgs
Correct answer: D
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100 kgs of an alloy of tin and lead in the ratio 1:3 is mixed with x k Updated on: 16 Apr 2020, 02:36
Originally posted by Enchanting on 15 Apr 2020, 09:21.
Last edited by Enchanting on 16 Apr 2020, 02:36, edited 1 time in total.
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Bunuel
100 kgs of an alloy of tin and lead in the ratio 1:3 is mixed with x kgs of an alloy of tin and lead in the ratio 3:2. If the overall alloy should contain between 40% and 50% tin, what is the range of values x can take?

A. 100 kgs ≤ x ≤ 200 kgs
B. 110 kgs ≤ x ≤ 240 kgs
C. 105 kgs ≤ x ≤ 220 kgs
D. 75 kgs ≤ x ≤ 250 kgs
E. 60 kgs ≤ x ≤ 150 kgs

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    The ratio of tin and lead in 100 kg alloy = 1: 3
      Amount of tin = \(\frac{100}{4}*1 = 25\) kg
      Amount of lead = \(\frac{100}{4}*3 = 75\) kgs
    The ratio of tin and lead in x kg = 3: 2
      Amount of tin = \(\frac{x}{5}*3 =\frac{3x}{5}\) kg
      Amount of lead = \(\frac{x}{5}*2 = \frac{2x}{5}\) kg
    Total amount of alloy = \(100 + x\)
      Overall amount of tin =\(25 + \frac{3x}{5}\)
    Now, If the overall tin is 40%
      Then, \(\frac{40}{100}*(100+x) = 25 + \frac{3x}{5}\)
      \(40 + \frac{2x}{5} = 25 + \frac{3x}{5}\)
      \(40 – 25 = \frac{3x}{5} – \frac{2x}{5}\)
      \(15*5 = x\)
      \(x = 75\) kg
    If the overall tin = 50%
      Then,\( \frac{50}{100}*(100+x)=25 + \frac{3x}{5}\)
      \(50 + \frac{x}{2} = 25 +\frac{3x}{5}\)
      \(50 – 25 = \frac{6x}{10} – \frac{5x}{10}\)
      \(25*10 = x\)
      \(x = 250\)
    Thus, \(75 kg ≤ x≤ 250kg\)
Answer: Option D.
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100 kgs of an alloy of tin and lead in the ratio 1:3 is mixed with x k 15 Apr 2020, 14:01
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100 kgs of an alloy of tin and lead in the ratio 1:3 is mixed with x kgs of an alloy of tin and lead in the ratio 3:2. If the overall alloy should contain between 40% and 50% tin, what is the range of values x can take?

Case1: if the overall alloy should contain 40% tin:

25%-----40%----------60% (x kgs)
(100 kgs)
--> \(\frac{x}{100}= \frac{(40-25)}{(60-40)}= \frac{15}{20}= \frac{3}{4}\)
\(x= \frac{300}{4}= 75\)

Case2: if the overall alloy should contain 50% tin:

25%-------------50%------60% (x kgs)
(100 kgs)

--> \(\frac{x}{100}= \frac{(50-25)}{(60-50)}= \frac{25}{10}= \frac{5}{2}\)
\(x= \frac{100*5}{2}= 250\)

The range of values of x
\(75 < x < 250\) kgs

Answer (D).
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100 kgs of an alloy of tin and lead in the ratio 1:3 is mixed with x k 26 Oct 2025, 11:19
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