Question 276702
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Let's illustrate the tank to help us in the problem:
{{{drawing(300,300,-1,2,-1,5,line(0,0,0,4),line(0,4,1,4),line(1,4,1,0),line(1,0,0,0), green(line(0,1.2,1,1.2)), green(line(0,1.2,1,1.2)), green(line(0,1.15,1,1.15)), green(line(0,1.1,1,1.1)), green(line(0,1,1,1)),green(line(1,0.95,1,0.95)),green(line(0,.90,1,0.90)),green(line(0,.85,1,.85)), green(line(0,.8,1,.8)),green(line(0,.75,1,.75)),green(line(0,.7,1,.7)),green(line(0,.65,1,.65)),green(line(0,.6,1,.6)),green(line(0,.55,1,.55)),green(line(0,.5,1,.5)),green(line(0,.45,1,.45)),green(line(0,.40,1,.4)),green(line(0,.35,1,.35)),green(line(0,.3,1,.3)),green(line(0,.25,1,.25)),green(line(0,.2,1,.2)),green(line(0,.15,1,.15)),green(line(0,.1,1,.1)),green(line(0,.05,1,.05)),arrow(-.2,0,-.2,1.2),red(arrow(-.9,0,-.9,4)), red(locate(-.55,.7,(3/10)(x))),red(locate(-.8,3,x)))}}} ----> "+" 10 gal ---> {{{drawing(300,300,-1,2,-1,5,line(0,0,0,4),line(0,4,1,4),line(1,4,1,0),line(1,0,0,0), green(line(0,1.2,1,1.2)), green(line(0,1.2,1,1.2)), green(line(0,1.15,1,1.15)), green(line(0,1.1,1,1.1)), green(line(0,1,1,1)),green(line(1,0.95,1,0.95)),green(line(0,.90,1,0.90)),green(line(0,.85,1,.85)), green(line(0,.8,1,.8)),green(line(0,.75,1,.75)),green(line(0,.7,1,.7)),green(line(0,.65,1,.65)),green(line(0,.6,1,.6)),green(line(0,.55,1,.55)),green(line(0,.5,1,.5)),green(line(0,.45,1,.45)),green(line(0,.40,1,.4)),green(line(0,.35,1,.35)),green(line(0,.3,1,.3)),green(line(0,.25,1,.25)),green(line(0,.2,1,.2)),green(line(0,.15,1,.15)),green(line(0,.1,1,.1)),green(line(0,.05,1,.05)),arrow(-.2,0,-.2,3.2),red(arrow(-.9,0,-.9,4)), red(locate(-.5,2.8,(4/5)(x))),red(locate(-.8,3,x)), green(line(0,3.2,1,3.2)))}}} 


Putting the scenario into equation:
{{{(3/10)(x)+10gal=(4/5)(x)}}}
{{{10=(4/5)(x)-(3/10)(x)
{{{10=(x)(4/5-3/10)}}}
{{{10=(x)((8-3)/10)}}}
{{{10=(x)(5/10)=(x)(1/2)}}}
{{{highlight(x=2*10=20gal)}}}, Answer (full tank)


Check:
1st scenario
({{{3/10}}}) full = {{{(3/10)(20)=60/10=6gal}}}
2nd scenario: added 10 gal:
{{{6gal+10gal=16gal}}}


--> {{{16gal/20gal=4/5}}}


Thank you,
Jojo</font>