Answer:
The answer is B: The mixture has less than the intended volume, and more than the intended percent of butterfat
Step-by-step explanation:
The question involves comparing the point L to where it lies in relation to the two equations/lines, and in particular, thinking in terms of inequalities.
Note that the coordinates of point L are (350, 100). i.e. x = 350ml, and y = 100 ml, where x refers to the volume of whipping cream, and y refers to the volume of milk.
Now, let's first look at where L lies in relation to line b, and what this tells us about the point L:
1. Line b:
Note that line b gives the equation for the requirement that total volume of the mixture is 500ml.
One way to see how L relates to this line is to see that L is 'below' line b, which means it is in the region corresponding to the inequality
x + y < 500.
Thus the volume of L is less than the intended volume of Y.
However, if you are not yet familiar with how to graph inequalities, you can also just use the coordinates of L to directly calculate the volume:
i.e. Its volume is simply 350ml + 100 ml = 450 ml.
And so, since 450 < 500, this means the volume of L is less the the intended volume of 500ml.
Now let's look at point L in relation to Line a, and see what we can conclude:
2. Line a
Note that line a gives the equation for the requirement that the butterfat of the 500mL mixture is 12%, given whipping cream is %18 butterfat and some milk that is %4 butterfat.
As with the previous part, one way to conclude what the butterfat percentage of L is in relation to the required 12% butterfat, is to note that L is on the side of line a the corresponds to the inequality
0.18x +0.04y > 0.12x500.
(Again, this involves understanding how to graph inequalities).
However we have to be slightly careful here as line a is the graph corresponding to 12 % of the volume of 500. But as we just found, the volume of L is actually 450. So we would need to actually re-draw a new line for the equation
0.18x +0.04y > 0.12x450,
and then compare L in relation to this. While this is one method that would work if continued, at this point, it would be quickest to instead just directly calculate the % of butter fat for L.
We can do this as follows:
Recall that cream is 18% butterfat, while milk is 4% butterfat, and that L is made up of 350 ml of cream and 100 ml of milk.
So the total amount of butterfat for L is:
0.18 x 350 + 0.04 x 100 = 67ml.
Next, we calculate 12% of the volume of L, i.e 12% of 450:
0.12 x 450 = 54ml
So, since 67 is greater than 54, this means the volume of butter fat in L is greater than 12 %.
Thus the answer is B: The mixture has less than the intended volume, and more than the intended percent of butterfat
