SOLUTION: Hi! A biologist has two brine solutions, one containing 1% salt and another containing 4% salt. How many milliliters of each solution should he mix to obtain 1 L of a solution t

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Question 200265: Hi!
A biologist has two brine solutions, one containing 1% salt and another containing 4% salt. How many milliliters of each solution should he mix to obtain 1 L of a solution that contains 2.8% salt?
thanks for the homework help!

Found 2 solutions by jim_thompson5910, MathTherapy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let

x = amount of brine solution with 1% salt (in liters)
y = amount of brine solution with 4% salt (in liters)


Since he's mixing the two solutions to get one liter, this means that x%2By=1. In other words, the two solutions add up to one liter.


So the first equation is x%2By=1


Since "x" is the amount of the 1% solution, this means that 0.01x is the amount of pure salt (since 1% of the given solution is given to be salt). Also, 0.04y is the amount of pure salt (from the other solution). These figures add up to the total 0.028%28x%2By%29 (note: 0.028 is the percentage while x+y is the total amount). Now add up the two parts and set them equal to the last portion to get 0.01x%2B0.04y=0.028%28x%2By%29


0.01x%2B0.04y=0.028%28x%2By%29 Start with the given equation.


0.01x%2B0.04y=0.028x%2B0.028y Distribute


10x%2B40y=28x%2B28y Multiply EVERY number by 1000 (to move the decimal 3 spots to the right)


10x%2B40y-28x-28y=0 Get everything to one side


-18x%2B12y=0 Combine like terms.


So the second equation is -18x%2B12y=0




So we have the system of equations:

system%28x%2By=1%2C-18x%2B12y=0%29


18%28x%2By%29=18%281%29 Multiply the both sides of the first equation by 18.


18x%2B18y=18 Distribute and multiply.


So we have the new system of equations:

system%2818x%2B18y=18%2C-18x%2B12y=0%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%2818x%2B18y%29%2B%28-18x%2B12y%29=%2818%29%2B%280%29


%2818x%2B-18x%29%2B%2818y%2B12y%29=18%2B0 Group like terms.


0x%2B30y=18 Combine like terms.


30y=18 Simplify.


y=%2818%29%2F%2830%29 Divide both sides by 30 to isolate y.


y=3%2F5 Reduce.


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18x%2B18y=18 Now go back to the first equation.


18x%2B18%283%2F5%29=18 Plug in y=3%2F5.


18x%2B54%2F5=18 Multiply.


5%2818x%2B54%2Fcross%285%29%29=5%2818%29 Multiply both sides by the LCD 5 to clear any fractions.


90x%2B54=90 Distribute and multiply.


90x=90-54 Subtract 54 from both sides.


90x=36 Combine like terms.


x=36%2F90 Divide both sides by 54 to isolate x.


x=2%2F5 Reduce.


So the solutions are x=2%2F5 and y=3%2F5.


Which form the ordered pair .


These solutions in decimal form are x=0.4 and y=0.6


Now recall that we stated that the values of "x" and "y" are in units of liters. So this means that x=0.4 liters and y=0.6 liters


Multiply both values by 1000 to convert to milliliters: 1000*0.4=400, 1000*0.6=600


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Answer:


So this means that 400 milliliters of the 1% salt solution and 600 milliliters of the 4% salt solution are needed to make a 1 L solution that is 2.8% salt.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Since the 2 solutions must add to 1 liter, then they must add to 1,000 ml
Let the amount of 1% salt solution in the 2.8% salt solution be x.
Then the amount of 4% solution in the 2.8% salt solution is 1,000 – x

Therefore, we get: .01(x) + .04(1,000 – x) = .028(1,000)

This equation becomes: .01x + 40 - .04x = 28
-.03x + 40 = 28
-.03x = - 12
x++=++%28-12%29%2F%28-.03%29 = 400
Therefore, he needs to mix 400 ML of the 1% salt solution, and 600 (1,000 – 400) ML of the 4% salt solution to get 1,000 ML, or 1 Liter of 2.8% salt solution.