Question 927909
Assuming we don't know the gallons of the 21% acid solution, we will express it as x.
Assuming we don't know the gallons of the 29% acid solution, we will express it as y.
In the assumptions, we are able to convey this equation.
{{{ x + y = 8 }}}
{{{ .21x + .29y = .26(8) }}}
We are able to solve it through substitution by finding that y = 8 - x through the subtraction property of equality.
{{{ .21x + .29(8-x) = .26(8) }}} Substitution
{{{ 21x + 29(8-x) = 26(8) }}} Since they are a percent, we will multiply all by 100.
{{{ 21x + 232 - 29x = 208 }}} Distribution
{{{ -8x + 232 = 208 }}} Combine Like Terms
{{{ -8x + 232 - 232 = 208 - 232 }}} Subtraction Property of Equality
{{{ -8x/-8 = -24/-8 }}} Division Property of Equality
{{{ x = 3 }}}
Now we know that x is 3, we will plug-in the x for the y to find the value of y.
{{{ y = 8 - x }}}
{{{ y = 8 - 3 }}}
{{{ y = 5 }}}

It takes 3 gallons of a 21% acid solution and 5 gallons of a 29% acid solution to make 8 gallons of a 26% acid solution.