## anonymous 4 years ago 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?

1. anonymous

2. anonymous

yea lol

3. 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 $.25(30+x)$

4. 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

5. 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

6. anonymous

okay thank you i really needed that i understand now.

7. anonymous

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

8. anonymous

oh alright.

9. 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

10. 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