A biologist has 40% solution and 10% solution of the same plant nutrient. How many cubic centimeters of each should be mixed to obtain 25 cc of 16% solution?
If x cc are 40%, then the rest (25-x) is 10%. So, adding up the nutrient content,
.40x + .10(25-x) = .16(25)
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A biologist has a 40% solution and a 10% solution of the same plant nutrient. How many cubic centimeters of each solution should be mixed to obtain 25 cc of a 22% solution?
By using math provided by Steve above, I got these answers with this equation:
0.40x + 0.10(25-x) = 0.22(25)
x = 25.46875 (or 815/32)
10.1875 cc of 40% solution
4.6875 cc of 10% solution
However these answers were counted wrong so I have no idea what to do now :/
Reply to Chloe
nvm im just stupid and didn't put a decimal for the 10%
x=10
4cc of 40%
1.5cc of 10%
these were also wrong so now im still confused ://///
Why did the plant nutrient become a mixologist? Because it wanted to whip up some 16% solution!
Now, let's solve this botanical mixology problem.
Let's say the biologist needs x cubic centimeters of the 40% solution and y cubic centimeters of the 10% solution to make 25 cc of the 16% solution.
So, we have two equations based on the concentration of the solutions:
Equation 1: (40% * x) + (10% * y) = 16% * 25 cc
Equation 2: x + y = 25 cc
Now, let's shake things up and solve for x and y:
From Equation 2, we know that x = 25 - y.
Substituting x in Equation 1, we have (40% * (25 - y)) + (10% * y) = 16% * 25 cc
Doing some calculations (and feeling like a math magician), we get:
(10 - 0.4y) + (0.1y) = 4
Combining like terms, we have:
-0.3y = -6
Dividing both sides by -0.3, we find:
y = 20
Now, substituting y in Equation 2, we get:
x + 20 = 25
Subtracting 20 from both sides, we find:
x = 5
So, the biologist needs to mix 5 cc of the 40% solution with 20 cc of the 10% solution to create 25 cc of the 16% solution. Happy mixing!
To solve this problem, we can use the method of mixtures.
Let's assume that x cubic centimeters of the 40% solution should be mixed and y cubic centimeters of the 10% solution should be mixed to obtain a total of 25 cc of the 16% solution.
We can calculate the amount of the nutrient in the final solution, which is 16% of 25 cc: (16/100) * 25 = 4 cc.
Now, we can set up an equation based on the nutrient amounts in each solution:
In the 40% solution, the nutrient occupies 40% of the solution. So, the amount of the nutrient in x cc of the 40% solution is (40/100) * x = 0.4x cc.
In the 10% solution, the nutrient occupies 10% of the solution. So, the amount of the nutrient in y cc of the 10% solution is (10/100) * y = 0.1y cc.
Since we want to obtain 4 cc of the nutrient in the final solution, the equation becomes:
0.4x + 0.1y = 4
We also have the constraint that the total volume of the solutions should be 25 cc:
x + y = 25
Now we can solve this system of two equations to find the values of x and y.
One way to solve this system is by substitution. Solve the second equation for x: x = 25 - y. Substitute this value of x into the first equation:
0.4(25 - y) + 0.1y = 4
Now, we can solve this equation algebraically:
10 - 0.4y + 0.1y = 4
Combining like terms:
-0.3y = -6
Divide both sides by -0.3:
y = 20
Now, substitute this value of y back into the equation x = 25 - y:
x = 25 - 20
x = 5
Therefore, to obtain a 25 cc solution with 16% nutrient concentration, you would need to mix 5 cc of the 40% solution and 20 cc of the 10% solution.