Question

1. How many mL of 70% and 40% alcohol elixirs

should be mixed to prepare 300 mL of 60%

alcohol?

Answer 1

that they are 200 mL of 70% and 100 mL of 40%

Explanation:

We have to build a 2x2 system of equations with the information from the statement as follows:

0.70 * x + 0.4 * y = 300 * 0.6

x + y = 300 => x = 300 - y

where x is elixir 1 (70%) and y elixir 2 (40%).

replacing we have:

0.70 * (300 - y) + 0.4 * y = 300 * 0.6

210 * - 0.7 * y + 0.4 * y = 180

-0.3 * y = 180 - 210

y = -30 / -0.3

y = 100

now for x:

x = 300 - 100

x = 200

Which means that they are 200 mL of 70% and 100 mL of 40%