If #20# quarts of milk contains #2# quarts of butter fat, how much pure water would be need to be added to the milk to make it #4%# butter fat?

1 Answer
Jun 13, 2017

Answer:

#color(red)(30)# quarts of pure water would need to be added.

Explanation:

Suppose that the required amount of water that would need to be added was #color(red)x# quarts.

The total resulting volume would be #color(blue)(20+color(red)x)#

The ratio of butter fat (given #color(green)2# quarts of butter fat) to total volume would be:
#color(white)("XXX")color(green)2/(color(blue)20+color(red)x)#

We are told that this ratio needs to be #color(magenta)(4%)#
and
Noting that #color(magenta)(4%)=color(magenta)(4/100)=color(magenta)(2/50)#

We have, as a requirement:
#color(white)("XXX")color(green)2/(color(blue)20+color(red)x)=color(magenta)(2/50)#

#rArr color(blue)(20+color(red)x)=color(green)50#

#rArr color(red)x= color(green)50-color(blue)20=color(red)30#