Question

A 40% vinegar solution is added to an 85% vinegar solution to create 1000 mL of a 60% solution.

How much of each solution is used?

Answer 1

Answer: To create a 1000 mL of a 60% vinegar solution, we need 600 mL of pure vinegar and 400 mL of water.

Let x be the amount of 40% vinegar solution and y be the amount of 85% vinegar solution used.

We know that:

x + y = 1000 mL (the total volume)

0.4x + 0.85y = 0.6(1000) (the amount of vinegar)

Solving for x and y:

x = (0.6(1000) - 0.85y) / 0.4

x + y = 1000

By substituting the first equation into the second, we get:

(0.6(1000) - 0.85y) / 0.4 + y = 1000

Solving for y:

y = 400 mL

x = (0.6(1000) - 0.85(400)) / 0.4 = 200 mL

So, 400 mL of 85% vinegar solution and 200 mL of 40% vinegar solution are used.

Explanation: