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- anonymous

Show an equation and a solution for the problem. Arnold needs a 25% solution of nitric acid. He has 20 milliliters (ml) of a 30% solution. How many ml of a 15% solution should he add to obtain the required 25% solution?

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- anonymous

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- anonymous

ready?

- anonymous

yea lol

- anonymous

ok he currently has 20 mg at 30% for a total of
\[.3\times 20=6\] mg of acid. lets say he adds "x" mg or 15% solution. then the total amount of solution he will have is
\[30+x\] and the "x" mg of 15% solution will contribute \[.15x\] acid. so he will have a total of
\[6+.15x\] acid, and a total of
\[30+x\] solution. now he wants that solution to be 255 acid, i.e. he want the total amount of acid to be
\[.25(30+x)\]

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- anonymous

now that we have two expressions for the amount of acid he wants, we can set them equal and write
\[6+.15x=.25(30+x)\] and solve for x

- anonymous

if you need help solving let me know, but i would get rid of the decimals first by multiplying both sides by 100 to write
\[600+15x=25(30+x)\]and work with whole numbers instead of decimals

- anonymous

okay thank you i really needed that i understand now.

- anonymous

and i see that i made a mistake, hold on a second

- anonymous

oh alright.

- anonymous

oh because i wasn't paying attention. he has 20 mg of 30% solution so the total amount is
\[20+x\] not what i wrote. equation should be
\[6+.15x=.25(20+x)\] i put a 30 instead of a 20

- anonymous

sorry about that. solve
\[600+15x=25(20+x)\]and you will get the answer. let me know if you have trouble but usually setting up the equation is the hard part, solving is the easy part

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