Answer
(a.)$1200-0.07x$.
(b.)$\$780$.
Work Step by Step
The given equation for the total interest earned at the end of the year is
$=0.05x+0.12(10,000-x)$
(a.) Apply distributive property.
$=0.05x+0.12\times 10,000-0.12\times x$
Simplify.
$=0.05x+1200-0.12x$
$=0.05x-0.12x+1200$
Apply distributive property.
$=(0.05-0.12)x+1200$
Simplify.
$=-0.07x+1200$
$=1200-0.07x$
(b.) From the question we have $x=\$6,000$.
Plug the value of $x$ into the resultant from part (a.).
$=1200-0.07(6,000)$
Clear the parentheses.
$=1200-420$
$=\$780$.
