Frank owns 250 acres of land. If he divides the land into 1/3 acre plots, how many plots will he have?

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Answer 1 · 2017-01-10T20:05:59

Total rewrite of solution:

250 acres has 750 plots.

This solution uses the same principle as in this example:

#1/2=2/4=4/8=8/16=50/100 larr" proportionality"#

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Given: 1 plot = #1/3# acres

Let the count of plots be #p#
Let the count of acres be #a#

We are given an initial condition of plots per acre.

The word 'per' means for each 1 of whatever it is referring to.

Mathematically this is written as #p/a#

So the initial condition is: #color(brown)(" "("plots")/("acres") -> p/a" "=" " (color(white)(.)1color(white)(.))/(1/3))#

The target is 250 acres so now we write #a# as 250:

#" "color(brown)(("plots")/("acres") -> p/a->" "p/250 = (color(white)(.)1color(white)(.))/(1/3))#

Multiply both sides by 250 to isolate #p#

#" "color(brown)(pxx250/250" "=" "(color(white)(.)1xx250color(white)(.))/(1/3))#

But #250/250=1# and # pxx1=p#

Also #250/(1/3)# is the same as #250xx3#

#" "color(brown)( p=250xx3 = 750 )#