You have $$50,000$ for investment. You will invest $S$ dollars in stocks and $B$ dollars in bonds. You expect a $10\%$ return on stocks and a $2\%$ return on bonds. You want a total return of $5\%$ on your investment.

$($a$)$ The dollar amount of the total return is $0\mathrm{.}0550,000=$$$2500.$ What is the dollar amount of return for stocks, and what is the dollar amount for bonds? $($Suggestion: Your answers will involve the variables $S$ and $B.)$

stocks $$ dollars

bonds $$ dollars

$($b$)$ Write a system of two equations in two unknowns that determines how much will be invested in each category. $($Suggestion: One equation should show the total amount invested. The second equation should show the total dollar return.$)$

$S+B=50,000$

$\mathrm{.}10S-\mathrm{.}02B=2500$

$S+B=2500$

$\mathrm{.}02S+\mathrm{.}10B=50,000$

$S+B=50,000$

$\mathrm{.}10S+\mathrm{.}02B=2500$

$S+B=2500$