Question

How much water do I need to addto l liters of pure alcohol to obtain asolution of 45% alcohol? write in an equation form

Answer 1

The perimeter of the rectangle is

`=24`

The length is

`=y`

The width is

`=x`

The formula to calculate the perimeter of a rectangle is given as

`=2(\text{length}+\text{width)}`

By substituting the values of the length, width, and perimeter above we will get the equation below

`\begin{gathered} perimeter=2(\text{length}+\text{width)} \\ 2(y+x)=24 \end{gathered}`

To talk about the length y in terms of x, we will make y the subject of the formula in the equation above

`\begin{gathered} 2(y+x)=24 \\ \text{divide both sides by 2} \\ (2(y+x))/(2)=(24)/(2) \\ y+x=12 \\ \text{therefore,} \\ y=12-x \end{gathered}`

Hence,

The length y in terms of x is given as y=12-x

To calculate the possible values of x and the possible values of y

The sum of x and y must give 12 therefore,

`\begin{gathered} \text{when x= 1} \\ y=12-x \\ y=12-1=11 \\ x=1,y=11 \end{gathered}`
`\begin{gathered} \text{when x=2} \\ y=12-x \\ y=12-2 \\ y=10 \end{gathered}`
`\begin{gathered} \text{when x=3} \\ y=12-x \\ y=12-3 \\ y=9 \end{gathered}`
`\begin{gathered} \text{when x=4} \\ y=12-x \\ y=12-4 \\ y=8 \end{gathered}`