Ana invests $$52,000$ received from her grandmother in three ways. With one part, she buys savings bonds at an interest rate of $1\mathrm{.}5\%$ per year. She uses the second part, which amounts to $6$ times the first, to buy mutual funds that offer a return of $6\%$ per year. She puts the rest of the money into a money market account paying $3\mathrm{.}5\%$ annual interest. The first year, her investments bring a return of $$2340.$ How much did she invest each way? $($Hint: For $1\mathrm{.}5\%$ interest, the amount of interest paid on $x$ dollars is $0\mathrm{.}015x.)$

Write a linear system of equations. Let $x$ be the first investment, $y$ be the second investment, and $z$ be the third investment. Choose the correct answer below.

A$.$

$x+y+z=6y$

$0\mathrm{.}015x+0\mathrm{.}06y+0\mathrm{.}035z=2340$

$6x=52,000$

c$.$

$x+y+z=52,000$

$0\mathrm{.}015x+0\mathrm{.}06y+0\mathrm{.}035z=2340$

$6x=y$

$B.$

$x+y+z=52,000$

$0\mathrm{.}015x+0\mathrm{.}06y+0\mathrm{.}035z=2340$

$6y=x$

D$.$

$x+y+z=2340$

$0\mathrm{.}015x+0\mathrm{.}06y+0\mathrm{.}035z=52,000$

$0\mathrm{.}08x=0\mathrm{.}06y$

Ana invested $$,$ at $1\mathrm{.}5\%,$$$,$ at $6\%,$ and $$,$ at $3\mathrm{.}5\%.$