Question

you need a 35% alcohol Solution on hand you have a 270 mL of a 30% alcohol mixture you also have 80% alcohol mixture how much of the 80% mixture will you need to add to obtain the desired solution

Answer 1

Step-by-step explanation:

Let 'x' be the amount of 80% alcohol solution needed.

The amount of alcohol in the 30% alcohol solution is:

`270\cdot(30)/(100)=270\cdot0.3=81ml`

The amount of alcohol in the 80% alcohol solution is:

`x\cdot(80)/(100)=x\cdot0.8`

The sum of these amounts is the amount of alcohol resulting of the mixture. We need the 35% of the final mixture be alcohol. This is:

`(270+x)(35)/(100)=(270+x)0.35`

So we have to solve the following equation for x:

`\begin{gathered} 270\cdot(30)/(100)+x\cdot(80)/(100)=(270+x)(35)/(100) \\ 81+0.8x=(270+x)\cdot0.35 \end{gathered}`

Solving we have:

`\begin{gathered} 81+0.8x=270\cdot0.35+0.35x \\ 81+0.8x-0.35x=94.5 \\ 0.45x=94.5-81 \\ x=(94.5-81)/(0.45) \\ x=30 \end{gathered}`

The total amount of the 35% alcohol solution obtained is:

`x+270=30+270=300mL`

Answer:

You will need 30 mL of the 80% alcohol solution.

The total amount of the 35% solution you'll obtain is 300mL