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

Question

Want to see more full solutions like this?

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.

Want to see more full solutions like this?

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

Students have asked these similar questions

2. Find the Bezier surface equation using the 9 control points shown below. Use the u and v directions shown. It is required to show all the calculation processes for finding Bernstein polynomials. Find the surface tangent, twist and normal vectors at point u=0.5 and v=0.5. (40 points) y 10 9 8 7 6 5 4 3 2 Poo и 1 1 2 3 4 5 6 7 8 9 10 10 X

3 00 By changing to circular coordinates, evaluate foo √²²+v³ dx dy.

A cable runs along the wall from C to P at a cost of $24 per meter, and straight from P to M at a cost of $26 per meter. If M is 10 meters from the nearest point A on the wall where P lies, and A is 72 meters from C, find the distance from C to P such that the cost of installing the cable is minimized and find this cost. C 72 P A 10 M

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.

Want to see more full solutions like this?

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

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.

Want to see more full solutions like this?

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

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.

Want to see more full solutions like this?

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.