How many gallons of milk containing 5% butter fat must be mixed with 100 gallons of 1% milk to obtain 2% milk?
Let x = number of gallons of %5 milk
0.05x + 0.01(100) = 0.02(x+100)
0.05x + 1 = 0.02(x+100)
0.05x + 1 = 0.02x + 2
0.03x = 1
x = 33 and 1/3
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To determine how many gallons of milk containing 5% butter fat must be mixed with 100 gallons of 1% milk to obtain 2% milk, we need to set up an equation based on the butter fat content.
Let x represent the number of gallons of milk containing 5% butter fat.
For the 5% milk:
The amount of butter fat in x gallons of 5% milk is 0.05x.
For the 1% milk:
The amount of butter fat in 100 gallons of 1% milk is 0.01 * 100 = 1 gallon.
For the 2% mixture:
The amount of butter fat in the resulting mixture of (x + 100) gallons is 0.02 * (x + 100) = 0.02x + 2 gallons.
Since we want to achieve a 2% mixture, we can set up the following equation:
0.05x + 1 = 0.02x + 2
Now we can solve for x:
0.05x - 0.02x = 2 - 1
0.03x = 1
x = 1 / 0.03
x ≈ 33.33
Therefore, approximately 33.33 gallons of milk containing 5% butter fat must be mixed with 100 gallons of 1% milk to obtain 2% milk.