help word problem

Question

Theresa Morgan, a chemist, has a 10% hydrochloric acid solution and a 55% hydrochloric acid solution. How many liters of each should she mix to get 1890 liters of a hydrochloric acid solution with a 50% acid concentration?

____liters of 10% hydrochloric acid solution .

 ____liters of 55% hydrochloric acid solution .

Geometry Dash

Answer 1

Let x = #liters of 10% solution

y = #liters of 55% solution

It must be true that x + y = 1890

This means y = 1890 - x (to be used later)

Now lets concentrate on the amount of acid in each beaker:

The 10% solution is x liters, so the amount of acid is 0.10x (10% of x)

The 55% solution is y liters, so the amount of acid is 0.55y (55% of y)

The final beaker contains x + y liters which is 1890 and that is supposed to contain 50% acid.

Final beaker contains 0.50(1890) = 1/2(1890) = 945 liters of acid in final mixture.

Set up the equation that models the fact that acid in 1st beaker + acid in 2nd beaker equals acid in mixture:

0.10x + 0.55y = 945

Since we do not like to work with decimals if we can avoid it, multiply every term by 100 to clear the decimals (not required).

10x + 55y = 94500

Now we use the equation referenced earlier, replacing y with 1890 - x (substitution method):

10x + 55(1890 - x) = 94500

10x - 55x + 55(1890) = 94500

55(1890) - 94500 = 55x - 10x

55(1890)-94500 = 45x

x = [55(1890) - 94500]/45 = 210

Since y = 1890 - x, y = 1890 - 210 = 1680

So, 210 liters of 10% solution and 1680 liters of 55% solution.

This should be true:

10% of 210 + 55% of 1680 equals 50% of 1890 (acid + acid equals total acid)

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