Question

Daniela invested a total of $50,000, some in a certificate of deposit (CD) and the remainder in bonds. The amount invested in bonds was $5,000 more than twice the amount she put into the CD. How much did she invest in each account? Call the amount that Daniela invested in the CD d and the amount she invested in bonds b.

Answer 1

Answer:

The amount invested in bonds = 35,000

The amount invested in CD = 15,000.

Step-by-step explanation:

The total amount that Daniela invested is $50,000, this means if we call the amount invested in bonds $b$, and the amount invested in CD $d$, then we have:

$b+d=50,000$ this says the total amount Daniela invested is $50,000.

And since the amount invested in bonds $b$ is $5,000 more than twice the amount Daniela put into the CD, we have:

$b=5,000+2d$.

Thus, we have two equations and two unknowns $b$ and $d$:

(1). $b+d=50,000$

(2). $b=5,000+2d$,

and we solve this system by substituting $b$ from the second equation into the first:

$b+d=50,000\\5,000+2d+d=50,000\\3d=45,000\\\\\boxed{d=15,000}$

or, the amount invested in CD is $15,000.

With the value of $d$ in hand, we now solve for $b$ from equation(2):

$b=5,000+2d\\b=5000+2(15,000)\\\boxed{b=35,000}$

or, the amount invested in bonds is $35,000.