Casper has some whipping cream that is 18\%18%18, percent butterfat and some milk that is 4\%4%4, percent butterfat. He wants to make a 500 mL mixture of them that is 12% butterfat. What does point L represent in this context?

At point L  the mixture has less than the intended volume, and more than the intended percent of butterfat

Step-by-step explanation:

Here is a proper format of the question for clarity

"Casper has some whipping cream that is %18 butterfat and some milk that is %4 butterfat. he wants to make a 500ml mixture of them that is 12% butterfat."

Please also see attached a graph that shows a system of equations for this scenario where x is the volume of whipping cream he uses and y is the volume of milk.

Step one:

let cream be x

and milk be y

The systems of equation for the situation is

0.18x+0.4y=0.12(500)------------1, this represents the requirement that the butterfat of the 500mL mixture is 12%,

x+y=500-------------------2 represents the volume of the mixture.

Now looking at the graph, the point L reads x=350 and y=100

Relating the point L to the volume we see that

350+100= 450

Therefore the point L describes a situation in which the volume is not as expected. because 450<500

Relating the point L to the requirement that the butterfat of the 500mL mixture is 12%,  

Because the volume was found to be 450L. we can re-write the expression for the volume as

0.18x +0.04y > 0.12x450,  

let us calculate  the total amount of butterfat for L is:

0.18 x 350 + 0.04 x 100 = 67ml.

12% of the volume of L, i.e 12% of 450:

0.12 x 450 =  54ml

67 is greater than 54, this means the volume of butterfat in L is greater than 12 %.

Hence the mixture has less than the intended volume, and more than the intended percent of butterfat

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step-by-step explanation: