Question

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

Answer 1

Total rewrite of solution:

250 acres has 750 plots.

Explanation:

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 )`