Question 877439
The "4 pint mixture of paint that is made up of equal amounts of blue paint and red paint" contains
{{{4pints/2=2pints}}} of blue paint, and
{{{4pints/2=2pints}}} of red paint.
 
a.
If {{{p}}} represents the number of pints of blue paint that will be in the new mixture,
{{{p-2}}} is the number of pints of blue paint that will be added to the "4 pint mixture of paint that is made up of equal amounts of blue paint and red paint."
{{{2}}} is the number of pints of red paint that will be in the new mixture,
because that is how much was in the original mixture and no red paint will be added.
Then, {{{p+2}}} is the total number of pints of paint (blue + red) that will be in the new mixture.
I do not know what the question asks for.
Is it asking for the number of pints of paint of each color? That would be {{{2}}}pints of red and {{{p}}} pints of blue.
Is it asking for the total number of pints of paint? That would be {{{p+2}}}pints of paint.
Why were you given the 65% blue paint target for the final mixture?
Are you expected to use that 65% to calculate further and find the value of {{{p}}} in a mixture containing 65% blue paint and made as described?
If the new mixture is 65% blue paint, then
{{{p/(p+2)=65/100}}} or {{{p/(p+2)=0.65}}}
{{{p=0.65(p+2)}}}-->{{{p=0.65p+1.3}}}-->{{{p-0.65p=1.3}}}-->{{{0.35p=1.3}}}-->{{{p=1.3/0.35}}}
That is {{{p=26/7=3&5/7=about 3.41}}} , which means that you would add about {{{1.41 pints of blue paint to the original mixture.
 
b.
For a final mixture being 60% blue paint, you would set up the equation
{{{p/(p+2)=60/100}}} or {{{p/(p+2)=0.6}}}