Question 22706
Let x = the number of gallons of 80% alcohol solution that are required to be mixed with 40 gallons of a 13% alcohol solution to obtain 40+x gallons of 70% alcohol solurtion. You can write the equation, after changing the percentages to their decimal equivalents:

{{{x(0.8) + 40(0.13) = (40+x)(0.7)}}} Simplify and solve for x.
{{{0.8x + 5.2 = 28 + 0.7x}}} Subtract 0.7x from both sides of the equation.
{{{0.1x + 5.2 = 28}}} Subtract 5.2 from both sides.
{{{0.1x = 22.8}}} Finally, divide boths sides by 0.1
{{{x = 228}}}gallons.