How much of a 5% acid solution should be added to 100ml of a 16% acid solution to dilute to an 7% acid solution?

Question

Can I get a step by step answer for the problem please?

Answer 1

Let x be the number of mL of 5% acid solution. In a 100mL of the 16% solution there will be 16mL. The total amount of mixture is 100+x mL. This has to be 7% acid. We can write the percentages as decimal fractions. 7% is 0.07 and 5% is 0.05. So 0.05x+16=0.07(100+x) mL.

So, 0.05x+16=7+0.07x. 16-7=0.02x, so 0.02x=9, x=9/0.02=900/2=450mL.

Therefore we need 450mL of 5% acid solution.

CHECK

450mL of 5% solution contains 22.5mL of acid. 100+450=550mL of mixture which is 7% acid=38.5mL.

22.5+16=38.5 mL which balances, confirming we need 450mL of 5% acid solution.