SOLUTION: Heavy cream is 36% butterfat, while whole milk contains only 4% butterfat. In order to make a delicious pint of ice cream, a recipe calls for 2 cups of a mixture that is 24% bu

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Heavy cream is 36% butterfat, while whole milk contains only 4% butterfat. In order to make a delicious pint of ice cream, a recipe calls for 2 cups of a mixture that is 24% bu      Log On


   



Question 806895: Heavy cream is 36% butterfat, while whole milk contains only 4% butterfat.
In order to make a delicious pint of ice cream, a recipe calls for 2 cups of a
mixture that is 24% butterfat. How many cups of heavy cream should be used to produce the correct butterfat percentage?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
It looks like heavy cream is added to whole milk
Let +a+ = cups of heavy cream needed
Let +b+ = cups of whole milk needed
----------------------------------
(1) +a+%2B+b+=+2+
(2) +%28+.36a+%2B+.04b+%29+%2F+2+=+.24+
----------------------------
(2) +.36a+%2B+.04b+=+.48+
(2) +36a+%2B+4b+=+48+
(2) +9a+%2B+b+=+12+
subtract (1) from (2)
(2) +9a+%2B+b+=+12+
(1) +-a+-b+=+-2+
+8a+=+10+
+a+=+5%2F4+
and, since
(1) +a+%2B+b+=+2+
(1) +b+=+3%2F4+
1 and 1/4 cups of heavy cream is needed
check:
(2) +9a+%2B+b+=+12+
(2) +9%2A%285%2F4%29+%2B+3%2F4+=+12+
(2) +45+%2B+3+=+48+
(2) +48+=+48+
OK