Question #267da

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Answer 1 · 2017-03-07T22:20:41

30 plants takes 9 gallons

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

$\frac{6}{20} = \frac{x}{30}$ $6/20=x/30$

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:
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Stage 1

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

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

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Stage 2

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

$color(white)(.)$

$x=9$ gallons