Find how many quarts of 6% butterfat milk and 3% butterfat milk should be mixed to yield 60 quarts of 4% butterfat milk.
1 answer:
Answer:
20 quarts of 6% butterfat milk and 40 quarts of 3% butterfat milk is used to make 60 quarts of 4% butterfat milk.
Step-by-step explanation:
We are given the following in the question:
Let x quarts of 6% butterfat milk be used and y quarts of 3% butterfat milk be used to make 60 quarts of 4% butterfat milk.
Thus, we can write the equation:
Total amount of 3% butterfat milk = 60
Thus, we can write the equation:
Solving the two equation, we get,
Thus, 20 quarts of 6% butterfat milk and 40 quarts of 3% butterfat milk is used to make 60 quarts of 4% butterfat milk.
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Part (i)
<h3>Answer: x^2 + 5x + 6</h3>-----------------
Work Shown:
(x+3)(x+2)
y(x+2) ..... Let y = x+3
y*x + y*2 ... distribute
x(y) + 2(y)
x(x+3) + 2(x+3) .... plug in y = x+3
x*x + x*3 + 2*x + 2*3 ... distribute
x^2 + 3x + 2x + 6
x^2 + 5x + 6
=====================================================
Part (ii)
<h3>Answer: 4x^2 - 16x + 7</h3>-----------------
Work Shown:
We could follow the same set of steps as shown back in part (i), but I'll show a different approach. Feel free to use the method I used back in part (i) if the visual approach doesn't make sense.
The diagram below is a visual way to organize all the terms. Many textbooks refer to it as "the box method" which helps multiply out any two algebraic expressions.
Each inner cell is found by multiplying the corresponding outer terms. For instance, in the upper left corner we have 2x*2x = 4x^2. The other cells are filled out the same way.
The terms in those four inner cells (gray boxes) are:
- 4x^2
- -14x
- -2x
- 7
The like terms here are -14x and -2x which combine to -16x, since -14+(-2) = -16.
We end up with the answer 4x^2-16x+7
