Question 124543
Let x = the required number of liters of pure alcohol to be added to the 7 liters of 10% alcohol solution to get (7+x) liters of 30% alcohol solution.
The 7 liters of 10% alcohol solution can be expressed as:
{{{7(0.1)}}} and we'll add x liters of 100% alcohol to this to get the (7+x)(0.3) liters.
So, here's the equation:
{{{7(0.1)+x = (7+x)(0.3)}}} Simplify and solve for x.
{{{0.7+x = 2.1+0.3x}}} Subtract 0.3x from both sides.
{{{0.7+0.7x = 2.1}}} Now subtract 0.7 from both sides.
{{{0.7x = 1.4}}} Finally, divide both sides by 0.7
{{{x = 2}}}
The chemist will need to add 2 liters of pure alcohol to the 7 liters of the 10% alcohol solution to obtain 9 liters of 30% alcohol solution.
Check:
{{{7(0.1)+2 = (7+2)(0.3)}}}
{{{0.7+2 = 9(0.3)}}}
{{{2.7 = 2.7}}}