Explanation Given Information: The 87 − octane gas and 95 − octane gas are blended to make a 10 − gal batch of 93 − octane gas. Formula used: The applied problems using system of equations can be solved through the following steps: Step 1: Understand the problem. Step 2: Define variables and frame equation. Step 3: Solve the equations. Step 4: Verify the solution. Step 5: State the solution. Calculation: Consider provided information about the blending of octane gas. The amount of each type of octane gas to be blended to make 10 − gal batch of 93 − octane gas is required. Define the variables to the two unknown variables. x = number of gallons of 87-octane gas y = number of gallons of 95-octane gas The provided information is organized in the form of a table as below: Gallons of octane gas Percent of isooctane (as a decimal) Number of gallons x 0.87 0.87 x y 0.95 0.95 y 10 0.93 0.93 ( 10 ) Frame the system of equations: When x number of gallons of 87 − octane gas and y number of gallons of 95 − octane gas is blended to form 10 − gal batch of 93 − octane gas, the equation is: x + y = 10 …… (1) The number of gallons of 87 − octane gas blended with number of gallons of 95 − octane gas to get a mixture of 0.93 ( 10 ) which is 9.3 . So, the equation is: So, another equation is: 0.87 x + 0.95 y = 9.3 …… (2) The system of two equations is: x + y = 10 And, 0.87 x + 0.95 y = 9.3 Solve the system of equations. In the provided system of equations, use the equation ( 1 ) and solve for y . So this would make it easier to substitute this into another equation and solve by substitution method. x + y = 10 Subtract x from both the sides of the equation. x + y − x = 10 − x y = 10 − x Now, substitute y = 10 − x in equation ( 2 )

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ISBN: 9781323235911

Author: BITTINGER

Publisher: Pearson Custom Publishing

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Chapter 13, Problem 28RE

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To calculate: The quantity of 87− octane gas and 95− octane gas required to be blended to make a 10−gal batch of 93− octane gas.

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Chapter 13, Problem 27RE

Chapter 13, Problem 29RE

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The quantity of 87 − octane gas and 95 − octane gas required to be blended to make a 10 − gal batch of 93 − octane gas.

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To calculate: The quantity of 87− octane gas and 95− octane gas required to be blended to make a 10−gal batch of 93− octane gas.

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