A and B are two salt solutions with different concentrations. Mixing

Question

A and B are two salt solutions with different concentrations. Mixing 200g of A and 100g of B makes a 4% salt solution, and mixing 100g of A and 200g of B makes a 3% salt solution. What are the concentrations of A and B?

A. 5%, 2% 
B. 6%, 4% 
C. 5%, 1% 
D. 6%, 2% 
E. 7%, 3%

KarishmaB · Accepted Answer

Responding to a pm:

Using WA formula

w1/w2 = (A2 - Aavg)/(Aavg - A1)

200/100 = (A2 - 4)/(4 - A1)
8 - 2*A1 = A2 - 4

100/200 = (A2 - 3)/(3 - A1)
3 - A1 = 2*A2 - 6

Solving the two equations, we get A1 = 5% and A2 = 2%

Answer (A)

nick1816 · Answer

\frac{200a+100b}{300}= 4

2a+b=12.....(1)

Also,  \frac{100a+200b}{300}= 3

a+2b=9.....(2)

a= 5 and b =2

satya2029 · Answer

Wa/Wb=2/1=B-4/4-A
8-2A=B-4
B+2A=12-(1)
and
Wa/Wb=1/2=B-3/3-A
3-A=2B-6
2B+A=9-(2)
From 1 and 2
A=5, B=2

MathRevolution · Answer

=>

Assume the percentages of the two salt solutions  A  and  B  are  a%  and  b% , respectively. We need to figure out the amount of salt for salt solution questions.

The amount of salt in  200g  of solution  A  is  200*(\frac{a}{100}) = 2a . The amount of salt in  100g  of solution  B  is  100*(\frac{b}{100}) = b.

After mixing the  2  solutions, the new solution is  \frac{(2a + b) }{ 300} = \frac{4}{100} ,  100(2a + b) = 4(300),  and  200a + 100b = 1200 . Dividing everything by  100  gives us  2a + b = 12.

Then, the amount of salt in  100g  of solution  A  is  100*(\frac{a}{100}) = a  and  200*(\frac{b}{100}) = 2b.

After mixing the  2  solution, the new solution is  \frac{(a + 2b) }{ 300} = \frac{3}{100,} 100(a + 2b) = 3(300),  and  100a + 200b = 900 . Dividing everything by  100  gives us  a + 2b = 9.

When we add two equations, we have  (2a + b) + (a + 2b) = 12 + 9, 3a + 3b = 21  or  a + b = 7. 
 
Then we have  a = (2a + b) - (a + b) = 12 – 7 = 5  and  b = (a + 2b) – (a + b) = 9 – 7 = 2.

Therefore, A is the answer
Answer: A

Kinshook · Answer

Let the concentration of A & B be a & b respectively

(200a + 100b)/300 = 4
(100a + 200b)/300 = 3

giving 
a = 5 & b = 2

IMO A

GradMentors · Answer

While I thought all the solutions provided were adequate, I just wanted to share my approach to the problem.

Let A = the concentration of solution A

Let B = the concentration of solution B

200A + 100B = 300(0.04) = 12

100A + 200B = 300(0.03) = 9

add them together

300A + 300B = 21

A+B = 21/300 = 0.07 ---> 7%

Only  Answer Choice A  is A+B equal to 7%

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A and B are two salt solutions with different concentrations. Mixing

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