Please help! I don't understand this brian is an agriculture scientist who is testing different applications of insecticides on tomato plants. For part of the trial he is running now he needs 125 gallons of 12% solution of test chemical AX-14. Brain received only containers with 7% solution and 15% concentrations of test chemical AX-14. How much of each chemical should brian mix to run his trial?

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Please help! I don't understand this brian is an agriculture scientist who is testing different applications of insecticides on tomato plants. For part of the trial he is running now he needs 125 gallons of 12% solution of test chemical AX-14. Brain received only containers with 7% solution and 15% concentrations of test chemical AX-14. How much of each chemical should brian mix to run his trial?

Mathematics
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HI!!
HI!
don't you hate word problems?
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we can still do it though, it is not that hard
haha yes very much!
we need a variable lets call the number of gallons of 15% solution \(x\) then since the total number of gallons of solution is 125, the amount of 7% solution is \(125-x\) so far so good?
this is where you say "yes i get it so far" or "no where did the \(125-x\) come from?"
okay i get it
ok the 15% part with \(x\) gallons gives \[0.15x\] solution and the remaining \(125-x\) gives \[0.07(125-x)\] and the total you want to be \(0.12\times 125\) solution
we can do this by solving \[0.15x+0.07(125-x)=0.12\times 125\] or get rid of the annoying decimal points and solve \[15x+7(125-x)=12\times 125\]
now it is a more or less routine linear equation to solve
okay so 15x+875-7x=12 x 125
yea now combine like terms etc
8x+875=12 x 125 -4x + 875=125 -4x=-750 x=187.5
i think there is a mistake somewhere here
the 12 got dropped somewheres
\[8x+875=1500\]
\[8x=625\]
oh yes i did somehow. it would be.. x=78.125
that is what i get too
okay thank you

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