solving the equation is so much easier than having to build it by a word problem :(

Question

A scientist needs 10 liters of a 20% acid solution for experiment, she only has a 5% solution and a 40% solution. To the nearest 10th of the liter, about how many liters of the 5% and the 40% solutions should she mix to get the solution she needs? write the equation.

Answer 1

We need 2 equations to solve for the 2 unknowns.

Let V₁ = volume of 5% solution and let V₂ = volume of 40% solution

The equations are as follows:

V₁ + V₂ = 10

(0.05 * V₁) + (0.4 * V₂) = 10 * 0.2 = 2

Let's solve by substituting one equation into the other:

V₁ = 10 - V₂

0.05(10 - V₂) +0.4V₂ = 2

0.5 - 0.05V₂ +0.4V₂ = 2

0.35V₂ = 1.5

V₂ = 4.3 liters

V₁ = 10 - 4.3 = 5.7 liters