Question

How many liters of 30% chemical solution must be mixed with 30 liters of 70% chemical solution to get a 60% mixture?

Answer 1

10 liters

Step-by-step explanation

We will assume the given percentages are those by volume (i.e. v/v).

We're asked to find the volume, in L, of a 30% v/v that must be added to 30 L of 70% solution v/v to obtain a solution that 60% v/v.

To do this, we can set up sort of an algebraic equation that represents this situation.

`\begin{gathered} (30)/(100)* L+(70)/(100)*30=(60)/(100)*(L+30) \\ \\ 0.3L+21=0.6(L+30) \\ \\ 0.3L+21=0.6L+18 \\ \\ Grouping\text{ }the\text{ }terms \\ \\ 0.6L-0.3L=21-18 \\ \\ 0.3L=3 \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }0.3 \\ \\ (0.3L)/(0.3)=(3)/(0.3) \\ \\ L=10\text{ }liters \end{gathered}`

Therefore, 10 liters of 30% chemical solution must be mixed with 30 liters of 70% chemical solution to get a 60% mixture