Question

Otto has some whipping cream that is
\[30\%\] butterfat and some milk that is
\[2\%\] butterfat. He wants to make a
\[500\,\text{mL}\] mixture of them that is
\[12\%\] butterfat.
Here's 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 he uses.
A graph with two lines and a point. Line A is labeled 0.30 times x plus 0.02 times y equals 0.12 times 500. Line B is labeled x plus y equals 500. Point J is on line A and above line B.
\[\small{200}\]
\[\small{400}\]
\[\small{600}\]
\[\small{200}\]
\[\small{400}\]
\[\small{600}\]
\[\small{800}\]
\[\small{1000}\]
\[y\,\text{(milk)}\]
\[x\,\text{(cream)}\]
\[\text{line }b: x+y=500\]
\[\text{line }a: 0.30x+0.02y=0.12(500)\]
\[J\]
What does point
\[J\] represent in this context?

Answer 1

Points on line A satisfy 0.30x + 0.02y = 60, so they are mixtures whose cream and milk together contain 60 mL of butterfat (12% of 500 mL). Point J, being on line A but not on line B, therefore represents a choice of x mL whipping cream and y mL milk that gives the correct amount of butterfat but does not total 500 mL (in fact it makes more than 500 mL). The actual required mixture would be the intersection of the two lines.