Question

How many liters each of a 50% acid solution and a 75% acid solution must be used to produce 70 liters of a 70% acid solution? (Round to two decimal places if necessary.)

Answer 1

We can express this as a system of equations.

Let x be the liters of the 50%-acid solution and y the liters of the 75%-acid solution.

We then need 2 equations to solve this.

One equation is the total amount of liters (70 liters) that is equal to the sum of the amount of each solution:

`x+y=70`

The second equation is the final concentration, that is a weighted average of the concentration of each solution:

`0.5\cdot x+0.75\cdot y=0.7\cdot70=49`

Then, we can solve this by substitution:

`x+y=70\longrightarrow y=70-x`
`\begin{gathered} 0.5x+0.75y=49 \\ 0.5x+0.75(70-x)=49 \\ 0.5+52.5-0.75x=49 \\ -0.25x=49-52.5 \\ -0.25x=-3.5 \\ x=(3.5)/(0.25) \\ x=14 \end{gathered}`

Then, we can calculate y as:

`y=70-x=70-14=56`

Answer: we need 14 liters of the 50% acid solution and 56 liters of the 75% acid solution.