How much low fat milk(1%) and whole milk(4%) should be mixed to make 5 gallons of reduced fat milk (2%)?
a =1%
5 -a = 4%
0.01a+ 0.04(5-a) = 5(0.02)
.0.01a+ 0.2 -0.04a = 0.1
-0.03a + .2 = 0.1
-0.03a + .2 -.2 = 0.1-0.2
-.03a = -.1
a = 10/3
4% = 5-a
5/3
10/3 mixed with low fat milk (1%)
5/3 mixed with whole milk(4%)
To determine the amounts of low fat milk (1%) and whole milk (4%) needed to make 5 gallons of reduced fat milk (2%), we need to set up an equation based on the mixture.
Let's assume x represents the amount of low fat milk (1%) in gallons, and y represents the amount of whole milk (4%) in gallons.
The total volume equation is:
x + y = 5
The fat content equation is:
(0.01x + 0.04y) / (x + y) = 0.02
Now we can solve this system of equations to find the values of x and y.
First, rearrange the total volume equation to solve for y:
y = 5 - x
Substitute this value of y into the fat content equation:
(0.01x + 0.04(5 - x)) / (x + (5 - x)) = 0.02
Simplify:
(0.01x + 0.2 - 0.04x) / 5 = 0.02
Combine like terms:
0.01x - 0.04x + 0.2 = 0.02 * 5
Simplify further:
-0.03x + 0.2 = 0.1
Subtract 0.2 from both sides:
-0.03x = -0.1
Divide by -0.03:
x = -0.1 / -0.03
Calculate:
x ≈ 3.33
Now substitute the value of x back into the total volume equation to find y:
3.33 + y = 5
Subtract 3.33 from both sides:
y = 5 - 3.33
Calculate:
y ≈ 1.67
Therefore, to make 5 gallons of reduced fat milk (2%), you would need to mix approximately 3.33 gallons of low fat milk (1%) and 1.67 gallons of whole milk (4%).
To determine the amounts of low-fat milk (1%) and whole milk (4%) needed to make 5 gallons of reduced-fat milk (2%), we can set up a proportion based on the fat content in each type of milk.
Let's assume 'x' is the amount of low-fat milk (1%) and 'y' is the amount of whole milk (4%) required.
1% milk contains 1 part fat for every 100 parts of milk, and 4% milk contains 4 parts fat for every 100 parts of milk.
Therefore, the equation representing the fat content in the mixed milk is:
(1/100)x + (4/100)y = (2/100)(5 x 128) (Note: 1 gallon is equivalent to 128 fluid ounces)
Simplifying the equation:
0.01x + 0.04y = 0.01(5 x 128)
0.01x + 0.04y = 0.64
Since we want to find the amounts of each type of milk needed to make 5 gallons of reduced-fat milk, we also know that:
x + y = 5 x 128
x + y = 640
Now we have a system of equations:
0.01x + 0.04y = 0.64
x + y = 640
There are different methods to solve this system of equations, such as substitution or elimination. Let's use the elimination method to find the values of 'x' and 'y'.
Multiplying the first equation by 100 to eliminate decimals:
1x + 4y = 64
Now, subtract the second equation from the first:
(1x + 4y) - (1x + 1y) = 64 - 640
3y = 576
Divide both sides of the equation by 3 to solve for 'y':
y = 192
Now we can substitute the value of 'y' back into the second equation to solve for 'x':
x + 192 = 640
x = 640 - 192
x = 448
Therefore, 448 fluid ounces (or 3.5 gallons) of low-fat milk (1%) and 192 fluid ounces (or 1.5 gallons) of whole milk (4%) should be mixed to make 5 gallons of reduced-fat milk (2%).