SOLUTION: One type of gasohol is 10% alcohol and another type is 35% alcohol. How much of each type must be mixed to obtain 400 gallons of a 25% alcohol mixture?

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Question 62496: One type of gasohol is 10% alcohol and another type is 35% alcohol. How much of each type must be mixed to obtain 400 gallons of a 25% alcohol mixture?
Found 4 solutions by checkley71, josmiceli, stanbon, venugopalramana:
Answer by checkley71(8403) About Me  (Show Source):
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400*.25=.10X+.35(400-X)
100=.10X+140-.35X
.25X=40
X=40/.25
X=160 GALLONS OF 10 % GASOHOL
400-160=240 GALLONS OF 35 % ALCOHOL
PROOF
400*.25=.10*160+.35*240
100=16+84
100=100

Answer by josmiceli(19441) About Me  (Show Source):
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a = gasohol 10% alcohol
b = gasohol 35% alcohol
.1a+%2B+.35b+=+.25%2A400
a+%2B+b+=+400
multiply 2nd equation by .1
.1a+%2B+.1b+=+40
subtract 2nd from 1st
.25b+=+60
b+=+240
a+%2B+b+=+400
a+%2B+240+=+400
a+=+160
240 gal of the .1 mixture and
160 gal of the .35 misture

Answer by stanbon(75887) About Me  (Show Source):
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One type of gasohol is 10% alcohol and another type is 35% alcohol. How much of each type must be mixed to obtain 400 gallons of a 25% alcohol mixture?
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Let amount of 10% solution be "x" gallons; this has 0.10x gals. of alcohol
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Amount of 35% solution is "400-x" gallons; this has 0.35(400-x)=140-0.35x gals
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EQUATION:
alcohol + alcohol = 25%(400) gallons
0.10x+140-0.35x=100
-0.25x=-40
x=160 gallons (amount of 10% solution)
400-x=240 gallons (amount of 35% solution)
Cheers,
Stan H.

Answer by venugopalramana(3286) About Me  (Show Source):
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One type of gasohol is 10% alcohol( T SAY) and another type is 35% alcohol(F SAY). How much of each type must be mixed to obtain 400 gallons of a 25% alcohol mixture?
T+F = 400 G......F = 400 - T G....................1
ALCOHOL IN T = T*10/100=0.1T G.....................2
ALCOHOL IN F = F*35/100=0.35F=0.35(400-T)=140-0.35T G.............3
TOTAL ALCOHOL IN THE MIX = 400*25/100=100 G.................4
HENCE
0.1T+140-0.35T=100
0.35T-0.1T=140-100=40
0.25T = 40
T=40/0.25=160 G............IS 10% ALCOHOL IN THE MIX
F=400-160=240 G............IS 35% ALCOHOL IN THE MIX