Question

How many liters each of a 20 % acid solution and a 30 % acid solution must be used to produce 90 liters of a 25 % acid solution? (Roundto two decimal places if necessary.)

Answer 1

Let x = volume of 20% solution=0.2

Let y = volume of 30% solution=0.3

Equation of total volume:

x + y = 90

Equation of amount of acid:

`\begin{gathered} 0.2x+0.3y=0.25(90) \\ 0.2x+0.3y=22.5 \\ Solve\text{ x+y = 90 , for x} \\ x=90-y \end{gathered}`

Substitute into the second equation

`\begin{gathered} 0.2(90-y)+0.3y=22.5 \\ 18-0.2y+0.3y=22.5 \\ 0.1y=22.5-18 \\ 0.1y=4.5 \\ \text{divide both side by 0.1} \\ (0.1y)/(0.1)=(4.5)/(0.1) \\ y=45 \\ \sin ce\text{ x=90-y} \\ x=90-45 \\ x=45 \end{gathered}`

Therefore 45 liters of 20% solution and 45 liters of 30% solution

Hence the volume of 20% acid = 45 litres

the volume of 30% acid = 45 litres