## A chemist has one solution that has 50% acid. She has another solution that is 25% acid. How many liters of the 50% acid solution should she

Question

A chemist has one solution that has 50% acid. She has another solution that is 25% acid. How many liters of the 50% acid solution should she combine to get 10 liters of a 40% acid solution?

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3 years 2021-08-17T05:02:58+00:00 1 Answers 11 views 0

Step-by-step explanation:

Let’s begin by assigning letters to represent our two unknowns:

x (liters of 25% solution)

y (liters of 50% solution)

Our system of equations will consist of two equations:

Equation #1 (total volume of solution)

Equation #2 (total concentration of acid)

Our total volume of solution is 10 liters, which can be expressed as the sum of our unknowns:

Equation #1:  x + y = 10

Our total concentration of acid can be expressed as the sum of the individual acid concentrations to make up the concentration of the final solution:

Equation #2:  (0.25)(x) + (0.50)(y) =

(0.40)(10)

We can use Equation #1 to express one unknown in terms of the other and then plug that expression into Equation #2 to solve for one of the unknowns:

x + y = 10

y = 10 – x

Now we’ll plug our expression for y in terms of x into Equation #2 and solve for x:

0.25(x) + 0.50(10 – x) = 0.40(10)

0.25x + 5 – 0.50x = 4

-0.25x = 4 – 5

-0.25x = -1

x = (-1)/(-0.25)

x = 4 (liters of 25% solution)

Now we’ll plug our value for x into Equation #1 and solve for y:

4 + y = 10

y  = 10 – 4

y = 6 (liters of 50% solution)

Finally, we will verify the correctness of our answers by plugging these values into Equation #2 to see if the sum of the component acid concentrations equals the final solution concentration:

0.25(4) + (0.50)(6) = 0.40(10)

1 + 3 = 4

4 = 4 (our answers are correct)