Answer
For the mangos $=\$45$.
For the avocados $=\$22$.
Work Step by Step
Let the amount the dealer paid for mangos $=x$.
and avocados $=y$.
Total paid $=\$67$.
$\Rightarrow x+y=67$ ...... (1).
Profit for mango $=20\%$ of $x$.
$=0.20x$
Loss for avocados $=2\%$ of $y$.
$=-0.02y$
Total profit $=\$8.56$.
$\Rightarrow 0.20x-0.02y=8.56$
Divide both sides by $0.02$.
$\Rightarrow \frac{0.20x}{0.02}-\frac{0.02y}{0.02}=\frac{8.56}{0.02}$
Simplify.
$\Rightarrow 10x-y=428$ ...... (2)
Add equation (1) and (2).
$\Rightarrow x+y+10x-y=67+428$
Add like terms.
$\Rightarrow 11x=495$
Divide both sides by $11$.
$\Rightarrow x=45$
Substitute the value of $x$ into equation (1).
$\Rightarrow 45+y=67$
Substract $45$ from both sides.
$\Rightarrow 45+y-45=67-45$
Simplify.
$\Rightarrow y=22$.
