Please Help Me With This Problem For My Daughter.?

Question

need help with this algebra problem.?

I student needs 30% hydrocloric acid for a chemistry experiment. How much 5% acid should be mixed with 160ml of 40% acid to get the 30% acid needed?

17 minutes ago - 3 days left to answer.

Answer 1

Ok, so... The answer you are looking for is the amount of the 5% acid to be added.  Call this amount "x".

x = the amount of 5% acid to be added to create a 30% acid

When you add some of the 5% acid, the total amount of acid is going to be 160 + x, because 160 is the original amount and x is the amount added.  So your goal is to figure out when 160 + x becomes a 30% solution, so your goal is: when you have 160+x amount of solution, what is the acid percentage?

Well you know that with the 160ml, you have 40% and with the xml, you have 5%, so the total percentage is going to be

0.4 * 160 + 0.05 * x, and you want that to equal 0.3.

Your equation then becomes:

0.4 * 160 + 0.05x = 0.3 * (160+x)

--> The percentage from your original solution plus the percentage from the amount added should be 30% of the total amount

this is the same as

64 + 0.05x = 0.3 * 160 + 0.3x

64 + 0.05x = 48 + 0.3x

subtract 48 from both sides and 0.05x from both sides to get:

16 = 0.25x

divide both sides by 0.25 to get

x = 64

You can see this is correct because your original solution was 64ml of acid and 160 ml total.  5% of 64 is 3.2.  So your total amount of solution is 160 + 64 = 224 and the total amount of acid is 64 + 3.2 = 67.2.  67.2 is 30% of 224.  (224 * 0.3 = 67.2)

Hope you followed that - these problems can be tough and even tougher to explain.