Find how many quarts of 4% butterfat milk and 1% butterfat milk should be mixed to yield 90 quarts of 2 % butterfat milk.
To solve this problem, we can set up an equation based on the principle of conservation of mass:
Let x be the number of quarts of 4% butterfat milk.
Let y be the number of quarts of 1% butterfat milk.
Given:
Total mixture = 90 quarts
Butterfat percentage in the mixture = 2%
We can now set up the equation:
4% butterfat milk + 1% butterfat milk = 2% butterfat milk
(0.04x + 0.01y) = 0.02 * 90
0.04x + 0.01y = 1.8
Since we have two unknowns, x and y, we need another equation to solve for both variables. We use the given information that the total mixture is 90 quarts:
x + y = 90
Now we have a system of two linear equations:
0.04x + 0.01y = 1.8
x + y = 90
We can solve this system of equations using the substitution or elimination method. Let's solve it using the elimination method:
Multiply the second equation by -0.01 to make the y terms cancel:
0.04x + 0.01y = 1.8
-0.01x - 0.01y = -0.9
Now add the two equations together:
0.04x - 0.01x = 1.8 - 0.9
0.03x = 0.9
Divide both sides by 0.03:
x = 30
Substitute this value of x back into the second equation:
30 + y = 90
y = 90 - 30
y = 60
Therefore, you should mix 30 quarts of 4% butterfat milk and 60 quarts of 1% butterfat milk to yield 90 quarts of 2% butterfat milk.
To solve this problem, we need to set up an equation based on the butterfat percentages and quantities of milk. Here's how we can calculate it step by step:
Let's assume x represents the number of quarts of 4% butterfat milk to be mixed, and y represents the number of quarts of 1% butterfat milk.
1. Set up the equation based on the butterfat percentages:
4%x + 1%y = 2% * 90
2. Convert percentages to decimals:
0.04x + 0.01y = 0.02 * 90
3. Simplify:
0.04x + 0.01y = 1.8
To continue solving this equation, you'll need another equation to help solve for x and y. However, in this case, we have extra information that can help simplify the problem.
Since we know that the total quantity of milk is 90 quarts, we can set up a second equation to relate x and y:
x + y = 90
Solving this system of equations will give us the values for x and y, which represent the number of quarts of each type of milk to be mixed.
To solve the system of equations, we can use substitution or elimination. I will use the elimination method.
Multiply the second equation by 0.04 (to match the coefficient of x in the first equation):
0.04x + 0.04y = 3.6
Now we can subtract the first equation from the modified second equation:
(0.04x + 0.04y) - (0.04x + 0.01y) = 3.6 - 1.8
0.04x - 0.04x + 0.04y - 0.01y = 1.8
0.03y = 1.8
y = 1.8 / 0.03
y = 60
Now that we know y=60, we can substitute this value back into one of the original equations:
x + 60 = 90
x = 90 - 60
x = 30
Therefore, you should mix 30 quarts of 4% butterfat milk and 60 quarts of 1% butterfat milk to yield 90 quarts of 2% butterfat milk.
let the amount of 4% milk be x
then the amount of 1% mild is 90-x
.04x + .01(90-x) = .02(90)
multiply by 100
4x + 1(90-x) = 2(90)
4x + 90 - x = 180
3x = 90
x = 30
add 30 quarts of 4% with 60 quarts of 1%