How to obtain 6 liters of a 40% solutions from a mixture of 20% dye solution and 50% dye solution.

Question

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Answer 1

Question

Chapter C, Problem 1P

To determine

To find:

How to obtain 6 liters of a 40% solutions from a mixture of 20% dye solution and 50% dye solution.

Expert Solution & Answer

Answer to Problem 1P

Solution:

2 liters of the 20% dye solution and 4 liters of the 50% dye solution should be mixed to obtain 6 liters of a 40% solution.

Explanation of Solution

General strategy for problem solving:

1. Understand the problem. During this step, become comfortable with the problem. Some ways of doing this are as follows:

Read and reread the problem.

Choose a variable to represent the unknown.

Construct a drawing whenever possible.

Propose a solution and check. Pay careful attention to how you check your proposed solution. This will help when writing an equation to model the problem.

2. Translate the problem into an equation.

3. Solve the equation.

4. Interpret the results: Check the proposed solution in the stated problem and state your conclusion.

Calculation:

We have to find how much 20% dye solution and 50% dye solution should be mixed to obtain 6 liters of a 40% solution.

Let x = the amount of the 50% of total solution; then

(6−x) = the amount of the 20% of total solution.

Now we have to solve the problem in to an equation.

The amount of acid in each solution can be found by multiplying the acid strength of each solution by the number of liters.

The following table summarizes the given information.

	No. of Liters · Acid Strength=Amount of acid
50% solution	x· 50%=0.50x
70% solution	(6-x)· 70%=0.70(6-x)
40% Solution needed	6 · 40%=0.40(6)

The amount of acid in the final solution is the sum of the amounts of acid in the two beginning solutions.

In words:	Acid in 50% solution	+Acid in 20% solution	= acid in 40% mixture
Translate:	0.50x	+0.20(6-x)	=0.40(6)

Now we have to solve the above equation.

0.50x+0.20(6−x)=0.40(6)

We have to apply the distributive property, ab+c=ab+ac

0.50x+1.2−0.2x=2.4

Now combine like terms

0.50x−0.2x=2.4−1.20.3x=1.2

Divide both sides by 0.3, we get

0.3x0.3=1.20.3x=4

Now we have to interpret the results.

The amount of the 50% of total solution (x) =4liters.

The amount of the 20% of total solution (6-x)=6−4=2 liters.

Conclusion:

If 4 liters of the 50% solution are mixed with 2 liters of the 20% solution, the result is 6 liters of a 40% solution.

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a) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in standard inequality form (with 3 variables and 4 constraints) and suppose that we have reached a point where we have obtained the following tableau. Apply one more pivot operation, indicating the highlighted row and column and the row operations you carry out. What can you conclude from your updated tableau? x1 x2 x3 81 82 83 84 81 -2 0 1 1 0 0 0 3 82 3 0 -2 0 1 2 0 6 12 1 1 -3 0 0 1 0 2 84 -3 0 2 0 0 -1 1 4 -2 -2 0 11 0 0-4 0 -8

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Answer 2

Question

Chapter C, Problem 1P

To determine

To find:

How to obtain 6 liters of a 40% solutions from a mixture of 20% dye solution and 50% dye solution.

Expert Solution & Answer

Answer to Problem 1P

Solution:

2 liters of the 20% dye solution and 4 liters of the 50% dye solution should be mixed to obtain 6 liters of a 40% solution.

Explanation of Solution

General strategy for problem solving:

1. Understand the problem. During this step, become comfortable with the problem. Some ways of doing this are as follows:

Read and reread the problem.

Choose a variable to represent the unknown.

Construct a drawing whenever possible.

Propose a solution and check. Pay careful attention to how you check your proposed solution. This will help when writing an equation to model the problem.

2. Translate the problem into an equation.

3. Solve the equation.

4. Interpret the results: Check the proposed solution in the stated problem and state your conclusion.

Calculation:

We have to find how much 20% dye solution and 50% dye solution should be mixed to obtain 6 liters of a 40% solution.

Let x = the amount of the 50% of total solution; then

(6−x) = the amount of the 20% of total solution.

Now we have to solve the problem in to an equation.

The amount of acid in each solution can be found by multiplying the acid strength of each solution by the number of liters.

The following table summarizes the given information.

	No. of Liters · Acid Strength=Amount of acid
50% solution	x· 50%=0.50x
70% solution	(6-x)· 70%=0.70(6-x)
40% Solution needed	6 · 40%=0.40(6)

The amount of acid in the final solution is the sum of the amounts of acid in the two beginning solutions.

In words:	Acid in 50% solution	+Acid in 20% solution	= acid in 40% mixture
Translate:	0.50x	+0.20(6-x)	=0.40(6)

Now we have to solve the above equation.

0.50x+0.20(6−x)=0.40(6)

We have to apply the distributive property, ab+c=ab+ac

0.50x+1.2−0.2x=2.4

Now combine like terms

0.50x−0.2x=2.4−1.20.3x=1.2

Divide both sides by 0.3, we get

0.3x0.3=1.20.3x=4

Now we have to interpret the results.

The amount of the 50% of total solution (x) =4liters.

The amount of the 20% of total solution (6-x)=6−4=2 liters.

Conclusion:

If 4 liters of the 50% solution are mixed with 2 liters of the 20% solution, the result is 6 liters of a 40% solution.

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Answer 3

Question

Chapter C, Problem 1P

To determine

To find:

How to obtain 6 liters of a 40% solutions from a mixture of 20% dye solution and 50% dye solution.

Expert Solution & Answer

Answer to Problem 1P

Solution:

2 liters of the 20% dye solution and 4 liters of the 50% dye solution should be mixed to obtain 6 liters of a 40% solution.

Explanation of Solution

General strategy for problem solving:

1. Understand the problem. During this step, become comfortable with the problem. Some ways of doing this are as follows:

Read and reread the problem.

Choose a variable to represent the unknown.

Construct a drawing whenever possible.

Propose a solution and check. Pay careful attention to how you check your proposed solution. This will help when writing an equation to model the problem.

2. Translate the problem into an equation.

3. Solve the equation.

4. Interpret the results: Check the proposed solution in the stated problem and state your conclusion.

Calculation:

We have to find how much 20% dye solution and 50% dye solution should be mixed to obtain 6 liters of a 40% solution.

Let x = the amount of the 50% of total solution; then

(6−x) = the amount of the 20% of total solution.

Now we have to solve the problem in to an equation.

The amount of acid in each solution can be found by multiplying the acid strength of each solution by the number of liters.

The following table summarizes the given information.

	No. of Liters · Acid Strength=Amount of acid
50% solution	x· 50%=0.50x
70% solution	(6-x)· 70%=0.70(6-x)
40% Solution needed	6 · 40%=0.40(6)

The amount of acid in the final solution is the sum of the amounts of acid in the two beginning solutions.

In words:	Acid in 50% solution	+Acid in 20% solution	= acid in 40% mixture
Translate:	0.50x	+0.20(6-x)	=0.40(6)

Now we have to solve the above equation.

0.50x+0.20(6−x)=0.40(6)

We have to apply the distributive property, ab+c=ab+ac

0.50x+1.2−0.2x=2.4

Now combine like terms

0.50x−0.2x=2.4−1.20.3x=1.2

Divide both sides by 0.3, we get

0.3x0.3=1.20.3x=4

Now we have to interpret the results.

The amount of the 50% of total solution (x) =4liters.

The amount of the 20% of total solution (6-x)=6−4=2 liters.

Conclusion:

If 4 liters of the 50% solution are mixed with 2 liters of the 20% solution, the result is 6 liters of a 40% solution.

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Answer 4

Question

Chapter C, Problem 1P

To determine

To find:

How to obtain 6 liters of a 40% solutions from a mixture of 20% dye solution and 50% dye solution.

Expert Solution & Answer

Answer to Problem 1P

Solution:

2 liters of the 20% dye solution and 4 liters of the 50% dye solution should be mixed to obtain 6 liters of a 40% solution.

Explanation of Solution

General strategy for problem solving:

1. Understand the problem. During this step, become comfortable with the problem. Some ways of doing this are as follows:

Read and reread the problem.

Choose a variable to represent the unknown.

Construct a drawing whenever possible.

Propose a solution and check. Pay careful attention to how you check your proposed solution. This will help when writing an equation to model the problem.

2. Translate the problem into an equation.

3. Solve the equation.

4. Interpret the results: Check the proposed solution in the stated problem and state your conclusion.

Calculation:

We have to find how much 20% dye solution and 50% dye solution should be mixed to obtain 6 liters of a 40% solution.

Let x = the amount of the 50% of total solution; then

(6−x) = the amount of the 20% of total solution.

Now we have to solve the problem in to an equation.

The amount of acid in each solution can be found by multiplying the acid strength of each solution by the number of liters.

The following table summarizes the given information.

	No. of Liters · Acid Strength=Amount of acid
50% solution	x· 50%=0.50x
70% solution	(6-x)· 70%=0.70(6-x)
40% Solution needed	6 · 40%=0.40(6)

The amount of acid in the final solution is the sum of the amounts of acid in the two beginning solutions.

In words:	Acid in 50% solution	+Acid in 20% solution	= acid in 40% mixture
Translate:	0.50x	+0.20(6-x)	=0.40(6)

Now we have to solve the above equation.

0.50x+0.20(6−x)=0.40(6)

We have to apply the distributive property, ab+c=ab+ac

0.50x+1.2−0.2x=2.4

Now combine like terms

0.50x−0.2x=2.4−1.20.3x=1.2

Divide both sides by 0.3, we get

0.3x0.3=1.20.3x=4

Now we have to interpret the results.

The amount of the 50% of total solution (x) =4liters.

The amount of the 20% of total solution (6-x)=6−4=2 liters.

Conclusion:

If 4 liters of the 50% solution are mixed with 2 liters of the 20% solution, the result is 6 liters of a 40% solution.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter C, Problem 1P

To determine

To find:

How to obtain 6 liters of a 40% solutions from a mixture of 20% dye solution and 50% dye solution.

Expert Solution & Answer

Answer to Problem 1P

Solution:

2 liters of the 20% dye solution and 4 liters of the 50% dye solution should be mixed to obtain 6 liters of a 40% solution.

Explanation of Solution

General strategy for problem solving:

1. Understand the problem. During this step, become comfortable with the problem. Some ways of doing this are as follows:

Read and reread the problem.

Choose a variable to represent the unknown.

Construct a drawing whenever possible.

Propose a solution and check. Pay careful attention to how you check your proposed solution. This will help when writing an equation to model the problem.

2. Translate the problem into an equation.

3. Solve the equation.

4. Interpret the results: Check the proposed solution in the stated problem and state your conclusion.

Calculation:

We have to find how much 20% dye solution and 50% dye solution should be mixed to obtain 6 liters of a 40% solution.

Let x = the amount of the 50% of total solution; then

(6−x) = the amount of the 20% of total solution.

Now we have to solve the problem in to an equation.

The amount of acid in each solution can be found by multiplying the acid strength of each solution by the number of liters.

The following table summarizes the given information.

	No. of Liters · Acid Strength=Amount of acid
50% solution	x· 50%=0.50x
70% solution	(6-x)· 70%=0.70(6-x)
40% Solution needed	6 · 40%=0.40(6)

The amount of acid in the final solution is the sum of the amounts of acid in the two beginning solutions.

In words:	Acid in 50% solution	+Acid in 20% solution	= acid in 40% mixture
Translate:	0.50x	+0.20(6-x)	=0.40(6)

Now we have to solve the above equation.

0.50x+0.20(6−x)=0.40(6)

We have to apply the distributive property, ab+c=ab+ac

0.50x+1.2−0.2x=2.4

Now combine like terms

0.50x−0.2x=2.4−1.20.3x=1.2

Divide both sides by 0.3, we get

0.3x0.3=1.20.3x=4

Now we have to interpret the results.

The amount of the 50% of total solution (x) =4liters.

The amount of the 20% of total solution (6-x)=6−4=2 liters.

Conclusion:

If 4 liters of the 50% solution are mixed with 2 liters of the 20% solution, the result is 6 liters of a 40% solution.

Answer 6

Chapter C, Problem 1P

To determine

To find:

How to obtain 6 liters of a 40% solutions from a mixture of 20% dye solution and 50% dye solution.

Expert Solution & Answer

Answer to Problem 1P

Solution:

2 liters of the 20% dye solution and 4 liters of the 50% dye solution should be mixed to obtain 6 liters of a 40% solution.

Explanation of Solution

General strategy for problem solving:

1. Understand the problem. During this step, become comfortable with the problem. Some ways of doing this are as follows:

Read and reread the problem.

Choose a variable to represent the unknown.

Construct a drawing whenever possible.

Propose a solution and check. Pay careful attention to how you check your proposed solution. This will help when writing an equation to model the problem.

2. Translate the problem into an equation.

3. Solve the equation.

4. Interpret the results: Check the proposed solution in the stated problem and state your conclusion.

Calculation:

We have to find how much 20% dye solution and 50% dye solution should be mixed to obtain 6 liters of a 40% solution.

Let x = the amount of the 50% of total solution; then

(6−x) = the amount of the 20% of total solution.

Now we have to solve the problem in to an equation.

The amount of acid in each solution can be found by multiplying the acid strength of each solution by the number of liters.

The following table summarizes the given information.

	No. of Liters · Acid Strength=Amount of acid
50% solution	x· 50%=0.50x
70% solution	(6-x)· 70%=0.70(6-x)
40% Solution needed	6 · 40%=0.40(6)

The amount of acid in the final solution is the sum of the amounts of acid in the two beginning solutions.

In words:	Acid in 50% solution	+Acid in 20% solution	= acid in 40% mixture
Translate:	0.50x	+0.20(6-x)	=0.40(6)

Now we have to solve the above equation.

0.50x+0.20(6−x)=0.40(6)

We have to apply the distributive property, ab+c=ab+ac

0.50x+1.2−0.2x=2.4

Now combine like terms

0.50x−0.2x=2.4−1.20.3x=1.2

Divide both sides by 0.3, we get

0.3x0.3=1.20.3x=4

Now we have to interpret the results.

The amount of the 50% of total solution (x) =4liters.

The amount of the 20% of total solution (6-x)=6−4=2 liters.

Conclusion:

If 4 liters of the 50% solution are mixed with 2 liters of the 20% solution, the result is 6 liters of a 40% solution.

Answer 7

Chapter C, Problem 1P

To determine

To find:

How to obtain 6 liters of a 40% solutions from a mixture of 20% dye solution and 50% dye solution.

Answer 8

Expert Solution & Answer

Answer to Problem 1P

Solution:

2 liters of the 20% dye solution and 4 liters of the 50% dye solution should be mixed to obtain 6 liters of a 40% solution.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

General strategy for problem solving:

1. Understand the problem. During this step, become comfortable with the problem. Some ways of doing this are as follows:

Read and reread the problem.

Choose a variable to represent the unknown.

Construct a drawing whenever possible.

Propose a solution and check. Pay careful attention to how you check your proposed solution. This will help when writing an equation to model the problem.

2. Translate the problem into an equation.

3. Solve the equation.

4. Interpret the results: Check the proposed solution in the stated problem and state your conclusion.

Calculation:

We have to find how much 20% dye solution and 50% dye solution should be mixed to obtain 6 liters of a 40% solution.

Let x = the amount of the 50% of total solution; then

(6−x) = the amount of the 20% of total solution.

Now we have to solve the problem in to an equation.

The amount of acid in each solution can be found by multiplying the acid strength of each solution by the number of liters.

The following table summarizes the given information.

	No. of Liters · Acid Strength=Amount of acid
50% solution	x· 50%=0.50x
70% solution	(6-x)· 70%=0.70(6-x)
40% Solution needed	6 · 40%=0.40(6)

The amount of acid in the final solution is the sum of the amounts of acid in the two beginning solutions.

In words:	Acid in 50% solution	+Acid in 20% solution	= acid in 40% mixture
Translate:	0.50x	+0.20(6-x)	=0.40(6)

Now we have to solve the above equation.

0.50x+0.20(6−x)=0.40(6)

We have to apply the distributive property, ab+c=ab+ac

0.50x+1.2−0.2x=2.4

Now combine like terms

0.50x−0.2x=2.4−1.20.3x=1.2

Divide both sides by 0.3, we get

0.3x0.3=1.20.3x=4

Now we have to interpret the results.

The amount of the 50% of total solution (x) =4liters.

The amount of the 20% of total solution (6-x)=6−4=2 liters.

Conclusion:

If 4 liters of the 50% solution are mixed with 2 liters of the 20% solution, the result is 6 liters of a 40% solution.

Answer 12

Ch. C - Prob. 1P Ch. C - Prob. 2P Ch. C - Prob. 3P Ch. C - Prob. 4P Ch. C - Prob. 1E Ch. C - Prob. 2E Ch. C - Prob. 3E Ch. C - Prob. 4E Ch. C - Prob. 5E Ch. C - Prob. 6E

How to obtain 6 liters of a 40% solutions from a mixture of 20% dye solution and 50% dye solution.

To find: How to obtain 6 liters of a 40% solutions from a mixture of 20% dye solution and 50% dye solution.

Answer to Problem 1P

Explanation of Solution

Want to see more full solutions like this?

Chapter C Solutions

To find:

How to obtain 6 liters of a 40% solutions from a mixture of 20% dye solution and 50% dye solution.