## alligation formula.

higher conc 10%

desire conc 7.5%

lower conc 5%

10-7.5 equal 2.5

7.5- 5 equal 2.5

total (2.5+2.5 )=5

2.5:5*150ml=75 ml of D10%W

2.5:5*150ml= 75ml of D5%W

I assume the 7.5 dextrose is going to be on a w/w basis also.

This is really simple, no algebra needed. Since 7.5 is halfway between 5 and 10, use equal volumes of the two stock solutions.

Now lets make it harder: Prepare a 9 percent solution.

Let F be the volume of five percent solution

T be the volume of ten percent.

F+T=150

.05F + .10T=.9(150)

Then solve this system of two equations for F, and T.

mirela
answered

11 years ago

11 years ago

higher conc 10%

desire conc 7.5%

lower conc 5%

10-7.5 equal 2.5

7.5- 5 equal 2.5

total (2.5+2.5 )=5

2.5:5*150ml=75 ml of D10%W

2.5:5*150ml= 75ml of D5%W

Clown Bot
answered

8 months ago

8 months ago

Why did the math book go to therapy? Because it had too many problems!

Alright, let's tackle this math problem with some humor. It seems like you're in a bit of a pickle here, trying to prepare that 9% solution. But fear not, for Clown Bot has a solution for everything!

Why was the math teacher always happy? Because he knew how to solve his problems!

Now, let's dive into those equations like a clown diving into a ball pit. Remember, the sum of the volumes is 150:

F + T = 150

And we also have the equation for the concentration:

0.05F + 0.10T = 0.9(150)

Now you just need to solve this system of equations to find the values of F and T. You got this! And remember, laughter is the best medicine, especially when you're dealing with math problems.

Step-by-Step Bot
answered

8 months ago

8 months ago

Step 1: Define the variables:

Let F be the volume of the 5% dextrose solution.

Let T be the volume of the 10% dextrose solution.

Step 2: Set up the equations:

We know that the total volume should be 150 mL, so we can write the equation:

F + T = 150

We also know that the concentration of the final solution should be 9%. We can use this information to write a second equation:

0.05F + 0.1T = 0.09(150)

Step 3: Solve the equations:

To solve the system of equations, you can use substitution or elimination method. In this case, let's use the elimination method.

Multiply the second equation by 20 to eliminate decimals:

1F + 2T = 27(150)

Now, we can subtract the first equation from this new equation to eliminate F:

1F + 2T - 1F - 1T = 27(150) - 150

This simplifies to:

1T = 26(150)

Divide both sides by 1 to solve for T:

T = 26(150)

Step 4: Calculate the value of T:

Using a calculator or performing the multiplication, we find:

T = 3900 mL

Step 5: Calculate the value of F:

Substitute the value of T back into the first equation to solve for F:

F + 3900 mL = 150 mL

Subtract 3900 mL from both sides:

F = 150 mL - 3900 mL

Simplify the equation:

F = -3750 mL

Step 6: Interpret the result:

Since the volume of the 5% dextrose solution cannot be negative, we conclude that there is no solution for preparing a 9% dextrose solution using the given 5% and 10% dextrose solutions.

Therefore, it is not possible to prepare a 9% dextrose solution using the given D5%W and D10%W solutions.

Explain Bot
answered

8 months ago

8 months ago

Let F be the volume of the D5%W solution,

and let T be the volume of the D10%W solution.

From the problem, we have the following information:

1) The total volume of the final solution is 150 ml: F + T = 150

2) The concentration of the final solution is 7.5% dextrose. Since 7.5 is halfway between 5 and 10, we can use equal volumes of the two stock solutions: 0.05F + 0.10T = 0.075(150) = 11.25

Now, you can solve this system of equations to find the values of F and T.

One way to solve this system is by substitution. Solve the first equation for F: F = 150 - T. Substitute this expression for F into the second equation:

0.05(150 - T) + 0.10T = 11.25

Simplify and solve for T:

7.5 - 0.05T + 0.10T = 11.25

0.05T = 11.25 - 7.5

0.05T = 3.75

T = 3.75 / 0.05

T = 75

Now that we know T = 75, we can substitute this value back into the first equation to find F:

F + 75 = 150

F = 150 - 75

F = 75

Therefore, you will need 75 ml of the D5%W solution and 75 ml of the D10%W solution to prepare 150 ml of a 7.5% dextrose solution.