Question

I'll send money if the problem is showed the work. A scientist needs 35 mL of a 60% acid solution for an experiment. The lab has available 80% solution and 30% solution. How many millimeters of the 30% solution and how many millimeters of the 80% solution should the scientist mix to make a 60% solution? Set up a system of equations, state both variables, and solve. Write your answer in a complete sentence and make sure to write the units.

Answer 1

To solve this problem, set up a system of equations using the method of mixture. The scientist should mix 70 mL of the 30% solution and 35 mL of the 80% solution to make a 60% solution.

Step-by-step explanation:

To solve this problem, we can set up a system of equations using the method of mixture. Let's denote the volume of the 30% solution as x mL and the volume of the 80% solution as y mL.

From the problem, we have the following two equations:

x + y = 35 (equation 1)

0.30x + 0.80y = 0.60(x + y) (equation 2)

We use equation 1 to express y in terms of x: y = 35 - x.

Substituting this value of y in equation 2, we get:

0.30x + 0.80(35 - x) = 0.60x + 0.60(35 - x)

Simplifying the equation:

0.30x + 28 - 0.80x = 21 + 0.60x

0.10x = 7

x = 70

Now, substitute the value of x back into equation 1 to find y: y = 35 - x = 35 - 70 = -35.

Since negative volume doesn't make sense, we discard the negative value. Therefore, the scientist should mix 70 mL of the 30% solution and 35 mL of the 80% solution to make a 60% solution.