Question 1189701: A farm has a very regular land which is to be divided in three parts; one for cattle, another for sow and the rest for enjoyment of the family, in a ratio 8:5:2, respectively. If there are 4,000 square feet for family pleasure, the whole farm has:
a)26,000 square feet
b)30,000 square feet
c)52,000 square feet
d)60,000 square feet
e)300,000 square feet
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the ratio 8 to 5 to 2 = cattle to sow to enjoyment, respectively.
that's 8 parts cattle, 5 parts sow, 2 parts enjoyment.
the total number of parts is 15.
the ratio of parts to the total is 8/15 for cattle, 5/15 for sow, 2/15 for enjoyment.
if we let x equal the total and the part for enjoyment = 2/15 of the total, then we get 2/15 * x = the part for enjoyment.
let e represent the part for enjoyment and we get e = 2/15 * x.
solve for x to get x = 15/2 * e
since e = 4000 square feet, we get x = 15/2 * 4000 = 30,000.
this says the whole farm has 30,000 square feet avalable to it.
cattle has 8/15 * 30,000 = 16,000 square feet available to it.
sow has 5/15 * 30,000 = 10,000 square feet available to it.
enjoyment has 2/15 = 4,000 square feet available to it.
total is 16,000 + 10,000 + 4,000 = 30,000
ratio is 16,000 to 10,000 to 4,000 which is simplified to 8000 to 5000 to 2000 which is simplified further to 8 to 5 to 2.
solution is confirmed to be good.
solution is the whole farm has 30,000 square feet available to it.
that's selection b.
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