A dairy needs 280 gallons of milk containing 7% butterfat how many gallons each of milk containing 8% butterfat and milk containing 4% butterfat must be used to obtain the desired 280 gallons
To find out how many gallons of milk containing 8% butterfat and milk containing 4% butterfat are needed to obtain 280 gallons of milk with 7% butterfat, we can set up the following equation:
Let x be the number of gallons of milk containing 8% butterfat.
Let y be the number of gallons of milk containing 4% butterfat.
The equation can be written as:
0.08x + 0.04y = 0.07(280)
To solve for x and y, we need to use simultaneous equations.
1. One equation is the equation we just set up: 0.08x + 0.04y = 0.07(280)
2. The other equation is based on the fact that the total gallons of milk will be 280: x + y = 280
Now, we can solve these equations simultaneously to find the values of x and y.
Start with the second equation:
x + y = 280
Rearrange it to solve for x:
x = 280 - y
Now substitute this expression for x in the first equation:
0.08(280 - y) + 0.04y = 0.07(280)
Distribute the 0.08:
22.4 - 0.08y + 0.04y = 19.6
Combine like terms:
-0.04y = 19.6 - 22.4
-0.04y = -2.8
Divide both sides by -0.04 to solve for y:
y = -2.8 / -0.04
y = 70
So, you need 70 gallons of milk containing 4% butterfat.
Now substitute this value of y back into the second equation to find x:
x + 70 = 280
x = 280 - 70
x = 210
Therefore, you need 210 gallons of milk containing 8% butterfat.
To summarize, you need 210 gallons of milk containing 8% butterfat and 70 gallons of milk containing 4% butterfat to obtain the desired 280 gallons of milk with 7% butterfat.