Explanation Given information: The solutions to be used are 0.3 % butterfat containing milk and 3.3 % butterfat containing milk. The total amount of the butterfat containing milk to be prepared is 300 gal . The volume percent of butterfat in the resulting solution is 1 % . Formula used: Amount of a pure substance present in a solution can be calculated using its volume percent in the solution as follows: V = ( V solution × V % ) 100 Here, V is the Amount of the pure substance present in the solution, V solution is the total amount of solution and V % is the volume percent of the substance in the solution. The substitution method can be used to solve a system of equations by using the following steps: Step 1: Express one variable in terms of another from one equation. Step 2: Substitute the expression derived in the previous step into the second equation. Step 3: Solve the derived equation for second variable. Step 4: Substitute the value of second variable derived in the previous step into the first equation for first variable. Calculation: Let the required amount of 0.3 % butterfat containing milk and 3.3 % butterfat containing milk in gal be x and y respectively. Calculate the amount of pure butterfat present in 0.3 % butterfat containing milk as follows: V = ( x × 0.3 ) 100 = 0 .003 x Calculate the amount of pure butterfat present in 3.3 % butterfat containing milk as follows: V = ( y × 3.3 ) 100 = 0 .033 y Calculate the amount of pure butterfat present in 300 gal of 1 % butterfat containing milk as follows: V = ( 300 gal × 1 ) 100 = 3 gal Express the given relationship between the amounts in terms of variables as follows: The total amount of the butterfat containing milk to be prepared is 300 gal gives first equation x + y = 300 ………… (1) The total amount of pure butterfat present in 300 gal of 1 % butterfat containing milk is 3 gal , the amount of pure butterfat present in 0

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ISBN: 9781266148941

Author: Miller

Publisher: MCG CUSTOM

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Chapter 4.4, Problem 26PE

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To calculate: The required amount of each type of milk need to produce 300 gal of 1% milk if skim milk has 0.3% butterfat and the whole milk that has 3.3% butterfat.

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Chapter 4.4, Problem 25PE

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The required amount of each type of milk need to produce 300 gal of 1 % milk if skim milk has 0.3 % butterfat and the whole milk that has 3.3 % butterfat.

Solution Summary: The author explains how the substitution method can be used to solve a system of equations.

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To calculate: The required amount of each type of milk need to produce 300 gal of 1% milk if skim milk has 0.3% butterfat and the whole milk that has 3.3% butterfat.

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