EBK PRECALCULUS W/LIMITS

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 7.2, Problem 50E

To determine

To find: The system of equations in which one equation represents the total amount of final mixture required and the other represents the amounts of 87− and 92− octane gasoline in the final mixture.

Expert Solution

Answer to Problem 50E

The required system of equations is:

x+y=5000.87x+0.92y=445

Explanation of Solution

Given information:

Five hundred gallons of 89− octane gasoline is obtained by mixing 87− octane gasoline with 92− octane gasoline.

Calculation:

Let x and y represent the number of gallons of 87− and 92− octane gasoline, respectively.

So the equation that represents the total amount of final mixture is x+y=500→(1) .

And the equation that represents the amounts of 87− and 92− octane gasoline in the final mixtureis 0.87x+0.92y=0.89(500)⇒0.87x+0.92y=445→(2) .

To determine

To graph: The graph represents the two equations in the same viewing window. Also, how does the amount of 92− octane gasoline change as the amount of 87− octane gasoline increases?

Expert Solution

Explanation of Solution

Given information:

The system of equations we found in previous part is:

x+y=5000.87x+0.92y=445 .

Graph:

Using Desmos graphing utility,

EBK PRECALCULUS W/LIMITS, Chapter 7.2, Problem 50E , additional homework tip 1

Interpretation:

As the amount of 87− octane gasoline increases, the amount of 92− octane gasoline decreases.

To determine

To find: The amount of each type of gasoline is required to obtain the 500 gallons of 89− octane gasoline.

Expert Solution

Answer to Problem 50E

300 gallons of 87-octane gasoline and 200 gallons of 92-octane gasoline are required to obtain 500 gallons of 89-octane gasoline.

Explanation of Solution

Given information:

The system of equations we found in previous part is:

x+y=5000.87x+0.92y=445 .

Graph:

Using Desmos graphing utility,

EBK PRECALCULUS W/LIMITS, Chapter 7.2, Problem 50E , additional homework tip 2

Interpretation:

The solution of the system of equations is (300,200) . Therefore, 300 gallons of 87-octane gasoline and 200 gallons of 92-octane gasoline are required to obtain 500 gallons of 89-octane gasoline.

Chapter 7.2, Problem 49E

Chapter 7.2, Problem 51E

Chapter 7 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - Prob. 15E Ch. 7.1 - Prob. 16E Ch. 7.1 - Prob. 17E Ch. 7.1 - Prob. 18E Ch. 7.1 - Prob. 19E Ch. 7.1 - Prob. 20E Ch. 7.1 - Prob. 21E Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Prob. 24E Ch. 7.1 - Prob. 25E Ch. 7.1 - Prob. 26E Ch. 7.1 - Prob. 27E Ch. 7.1 - Prob. 28E Ch. 7.1 - Prob. 29E Ch. 7.1 - Prob. 30E Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Prob. 34E Ch. 7.1 - Prob. 35E Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Prob. 39E Ch. 7.1 - Prob. 40E Ch. 7.1 - Prob. 41E Ch. 7.1 - Prob. 42E Ch. 7.1 - Prob. 43E Ch. 7.1 - Prob. 44E Ch. 7.1 - Prob. 45E Ch. 7.1 - Prob. 46E Ch. 7.1 - Prob. 47E Ch. 7.1 - Prob. 48E Ch. 7.1 - Prob. 49E Ch. 7.1 - Prob. 50E Ch. 7.1 - Prob. 51E Ch. 7.1 - Prob. 52E Ch. 7.1 - Prob. 53E Ch. 7.1 - Prob. 54E Ch. 7.1 - Prob. 55E Ch. 7.1 - Prob. 56E Ch. 7.1 - Prob. 57E Ch. 7.1 - Prob. 58E Ch. 7.1 - Prob. 59E Ch. 7.1 - Prob. 60E Ch. 7.1 - 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The system of equations in which one equation represents the total amount of final mixture required and the other represents the amounts of 87 − and 92 − octane gasoline in the final mixture.

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To find: The system of equations in which one equation represents the total amount of final mixture required and the other represents the amounts of 87− and 92− octane gasoline in the final mixture.

Answer to Problem 50E

Explanation of Solution

To graph: The graph represents the two equations in the same viewing window. Also, how does the amount of 92− octane gasoline change as the amount of 87− octane gasoline increases?

Explanation of Solution

To find: The amount of each type of gasoline is required to obtain the 500 gallons of 89− octane gasoline.

Answer to Problem 50E

Explanation of Solution

Chapter 7 Solutions