# Susan purchased some municipal bonds yielding 7% annually and some certificates of deposit yielding 9% annually. if Susan's investment amounts to $19,000 and the annual income is$1,590, how much money is invested in bonds and deposits?

Jun 30, 2018

Certificates of deposits =$.13000 Bonds =$.6000

#### Explanation:

Susan buys bonds worth =$.x She buys certificates of deposits worth =$.y

Yield from bond $= x \times \frac{7}{100} = \frac{7 x}{100}$
yield from certificates $= y \times \frac{9}{100} = \frac{9 y}{100}$

Then,

$x + y = 19000$ --------(1)
$\frac{7 x}{100} + \frac{9 y}{100} = 1590$ Multiplying both sides by 100, we get

$7 x + 9 y = 159000$ -----(2)

Solving equation(1) for $x$, we get $x = 19000 - y$

Substitute $x = 19000 - y$ in equation (2), we get

$7 \left(19000 - y\right) + 9 y = 159000$

$133000 - 7 y + 9 y = 159000$

$133000 + 2 y = 159000$

$2 y = 159000 - 133000 = 26000$

$y = \frac{26000}{2} = 13000$

$y = 13000$

Certificates of deposits =$.13000 Substitute $y = 13000$in equation (1) $x + 13000 = 19000$$x = 19000 - 13000 = 6000$Bonds =$.6000