Question 125956
Start by assigning a variable to the unknown quantity.
Let x = the required number of ounces (oz) of the 50% acetic acid solution that must be added to the 32 oz of 5% acetic acid solution to obtain (32+x) oz of 10% acetic acid solution. After changing the percentages to their decimal equivalents, you can write the equation to solve for x.
{{{0.5(x)+0.05(32) = (32+x)(0.1)}}} Simplify and solve for x.
{{{0.5x + 1.6 = 3.2 + 0.1x}}} Subtract 0.1x from both sides.
{{{0.4x+1.6 = 3.2}}} Subtract 1.6 from both sides.
{{{0.4x = 1.6}}} Finally, divide both sides by 0.4
{{{x = 4}}}
You will need to add 4 oz of the 50% acetic acid soltion to the 32 oz of 5% acetic acid solution to obtain 36 (32+4) oz of the 10% acetic acid solution.
Check:
{{{0.5x+0.05(32) = (32+x)(0.1)}}} Substitute x = 4.
{{{0.5(4)+1.6 = (32+4)(0.1)}}}
{{{2+1.6 = 36(0.1)}}}
{{{3.6 = 3.6}}}