Answer
Amount deposited that earns 2.5 percent interest = $\$10,000$
Amount deposited that earns 3 percent interest = $\$20,000$
Work Step by Step
Let
$x$ = amount invested that earns $2.5\%$ annual interest
$2x$ = amount invested that earns $3\%$ annual interest
RECALL:
The simple interest ($I$) earned is given by the formula:
$I=Prt$
where
P = principal/amount invested
r = annual interest rate
t = time
The in one year, the investments will earn an interest of:
at 2.5 percent:
$I=Prt
\\I=x(2.5\%)(1)
\\I=x(0.025)(1)
\\I=0.025x$
at 3 percent:
$I=Prt
\\I=(2x)(3\%)(1)
\\I=(2x)(0.03)(1)
\\I=0.06x$
Since te investments earn a total of $\$850$ in interest in one year, then
$0.025x + 0.06x = \$850
\\(0.025+0.06)x=\$850
\\0.085x = \$850
\\\dfrac{0.085x}(0.085)=\dfrac{\$850}(0.085)
\\x=\$10,000$
Thus,
$2x=2(\$10,000) = \$20,000$
Therefore the amount deposited are:
for the one that earns a 2.5 percent interest = $\$10,000$
for the one that earns a 3 percent interest = $\$20,000$
