A biologist has a 36% solution and a 14% solution of the same plant nutrient. How many cubic centimeters (cc) of each solution should be mixed to obtain a 25 cc of a 25% solution? I been looking at this for 2 hours please help
amount of 36% solution -- x cc
amount of 14% solution -- (25-x) cc
.36x +.14(25-x) = .25(25)
times 100 , (don't like decimals like to avoid them)
36x + 14(25-x) = 25(25)
36x - 14x = 625 - 350
22x = 275
x = 12.5 cc
so it looks like 12.5 cc of each
Thank you so much Reiny
The answer given above is wrong.
The formula used is incorrect.
To solve this problem, let's break it down into smaller steps.
Step 1: Define the variables.
Let's assume the biologist needs to mix x cubic centimeters (cc) of the 36% solution and y cubic centimeters (cc) of the 14% solution to obtain a 25 cc of a 25% solution.
Step 2: Write the equation based on the given information.
The equation for the nutrient content of the mixture can be expressed as:
0.36x + 0.14y = 0.25 * 25
This equation states that the sum of the nutrient content in the 36% solution (0.36x) and the 14% solution (0.14y) should be equal to the nutrient content in the resulting 25% solution (0.25 * 25).
Step 3: Solve the equation.
Let's solve the equation using substitution or elimination method.
Substitution Method:
Solve one of the equations for one variable (in this case, let's solve for x):
x = (0.25 * 25 - 0.14y) / 0.36
Plug this value of x into the other equation:
0.36 * [(0.25 * 25 - 0.14y) / 0.36] + 0.14y = 25
Simplify the equation:
9 * (0.25 * 25 - 0.14y) + 0.14y = 100
Expand:
56.25 - 1.26y + 0.14y = 100
Combine like terms:
-1.12y = 43.75
Divide by -1.12:
y ≈ -39.06
Substitute the value of y back into one of the original equations to find the value of x:
x = (0.25 * 25 - 0.14 * -39.06) / 0.36
x ≈ 11.61
Step 4: Check the solution.
Check if the solution satisfies all the given conditions:
- The total volume of the resulting solution should be 25 cc:
x + y ≈ 11.61 + (-39.06) ≈ -27.45
Since the volume cannot be negative, this solution is not valid.
Step 5: Revise the equation and solve again.
Since we cannot have a negative volume, it means we cannot mix any amount of the 14% solution with the 36% solution to obtain a 25% solution with a volume of 25 cc.
In this case, it seems that the information given is not sufficient, and it may not be possible to obtain the desired solution with the provided concentrations and volumes.