SOLUTION: A solution containing a 9% concentration of acid is mixed with a solution containing a 5% concentration of acid to get 100mL of solution containing an 8% concentration of acid. How

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Question 1151454: A solution containing a 9% concentration of acid is mixed with a solution containing a 5% concentration of acid to get 100mL of solution containing an 8% concentration of acid. How many mL of each solution is needed?
Found 2 solutions by addingup, jim_thompson5910:
Answer by addingup(3677) (Show Source):
You can put this solution on YOUR website!
0.09x + (100-x)*0.05 = 100*0.08
0.09x + 5-0.05x = 8
0.04x + 5 = 8
x = 3/0.04 = 75
You need 75mL of the 9% solution and 25mL of the 5% solution

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

Let's say we had two bottles of the acid.
Bottle A has 9% concentration of acid.
Bottle B has 5% concentration of acid.

We don't know how many mL of solution is in each bottle, so let,
x = amount of solution in bottle A
y = amount of solution in bottle B
Each bottle contains pure acid plus other stuff (either water only or other chemicals as well).

We want to mix the two bottles (A and B) so that we end up with 100 mL of total solution.
This means the amounts x and y must add to 100
x+y = 100

Solve for y to get
x+y = 100
x+y-x = 100-x
y = 100-x
We will use this equation later.

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From bottle A, we have 9% acid concentration. If we have x mL of solution in this bottle, then there is 0.09*x mL of pure acid here.

Inside bottle B is 0.05*y mL of pure acid because of the 5% concentration.

All together, there is 0.09x+0.05y mL of pure acid. Let's call this quantity C. So C = 0.09x+0.05y

We want to divide the value of C over 100 which was the total amount of solution we end up with when we mix the two bottles.

The expression C/100 is the percentage of pure acid in the final mixture.
We want this percentage to be 8%

So,
C/100 = 0.08
C = 100*0.08 ...... multiply both sides by 100
C = 8
0.09x+0.05y = 8 .... replace C with 0.09x+0.05y
0.09x+0.05( y ) = 8
0.09x+0.05( 100-x ) = 8 .... plug in y = 100-x
0.09x+0.05(100)+0.05(-x) = 8 .... distribute
0.09x+5-0.05x = 8
0.04x+5 = 8
0.04x+5-5 = 8-5 ..... subtract 5 from both sides
0.04x = 3
0.04x/0.04 = 3/0.04 .... divide both sides by 0.04
x = 75
We will need 75 mL of the 9% concentration

y = 100-x
y = 100-75 .... plug in x = 75
y = 25
and we need 25 mL of the 5% concentration.

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Answers:
75 mL of the 9% concentration
25 mL of the 5% concentration

As a check,
9% of 75 = 0.09*75 = 6.75 is the amount of pure acid from bottle A
5% of 25 = 0.05*25 = 1.25 is the amount of pure acid from bottle B
6.75+1.25 = 8 mL is the amount of pure acid in total after mixing both bottles
100 mL is the total amount of solution
8/100 = 0.08 = 8% is the proper concentration we're aiming for.
This helps confirm the answer