If 500 pounds of mush will feed 20 pigs for a week, for how many days will 200 pounds of mush feed 14 pigs?
Inversely proportional.
pig-days
First, you need to know how much a pig will eat each day.
If 500 lbs feeds 20 pigs for 7 days, then if we set up the ratio mush : day
.
So 20 pigs will eat lbs of mush per day.
Now we can set up another ratio of mush : pigs
.
So 14 pigs will eat 50 lbs of mush per day.
Finally, setting up the ratio mush : days
.
So 14 pigs will eat 200 lbs of mush in 4 days.
This is a tough question for the SAT. I would do it with a ratio (direct proportion) followed by an inverse proportion as follows:
First I'll answer this question: "If 500 pounds of mush will feed 20 pigs for a week, then 200 pounds of mush will feed how many pigs for a week?"
So
Now I'll answer this question: "If you can feed 8 pigs for 7 days, then for how many days can you feed 14 pigs?"
The problem is particularly confusing because there are three active variables here. I don't believe I've ever seen this in an actual SAT problem (if it ever did occur you could probably get it wrong and still get an 800). I have seen an additional inactive variable by which I mean the third variable wasn't needed to solve the problem (it was just there to confuse you). I'm curious what book this problem came from.