Question

Question #267da

Answer 1

30 plants takes 9 gallons

Explanation:

`color(blue)("Shortcut method")`

`6/20=x/30`

Multiply both sides by 30

`(6xx3cancel(0))/(2cancel(0))=x`

`x=18/2=9`

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`color(blue)("First Principles Method")`
Using ratio: this is another format for direct variation

Let the unknown volume in gallons be `x`

`("plants")/("water")->20/6-=30/x`

Just for the sake of convention turn everything upside down so that `x` is on the top. Not really necessary!

`("water")/("plants") ->6/20-=x/30` where `-=` means 'equivalent to'

Rather than do the jump in 1 go I am doing it in 2 stages:
.....................................................
Stage 1

`color(green)(6/20color(red)(xx1)" "=" "x/30)`

`color(green)(6/20color(red)(xx3/3)" "=" " 18/60" "-=" "x/30)`

..................................................................
Stage 2

`color(green)((18-:2)/(60-:2)=9/30=x/30`

`color(white)(.)`

`x=9` gallons