Question #267da

1 Answer
Mar 7, 2017

30 plants takes 9 gallons

Explanation:

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

6/20=x/30620=x30

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