Question

John wants to make a $100ml$ of $5$% alcohol solution mixing a quantity of a $2$% alcohol solution with a $7$% alcohol solution. That are the quantities of each of the two solutions ($2$% an d$7$%) he has to use?

Answer 1

Let $x$ and $y$ be the quantities of the 2% and 7% alcohol solutions to be used to make 100ml of 5%, here we get the equation as,
$x+y=100$
or $y=100-x$
Now to get the quantity of the solutions we get the equation as,
2%$x$$+$7%$y$ = 5%100
Now by substituting the value of $y$ in terms of $x$ we get,
2%$x$$+$7%$(100-x)$= 5%100
here by removing the % sign from both the sides we get,
$2x+7(100-x)=5\times 100$
$2x+700-7x=500$
$-5x=-200$
$x=40$
as we know $y=100-x$
$y=100-40$
$y=60$
Ans: to make a solution of 100ml 5% alcohol we will need 40ml of 2% and 60ml of 7% alcohol