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.

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

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

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

[tex]b=5,000+2d[/tex].

Thus, we have two equations and two unknowns [tex]b[/tex] and [tex]d[/tex]:

(1). [tex]b+d=50,000[/tex]

(2). [tex]b=5,000+2d[/tex],

and we solve this system by substituting [tex]b[/tex] from the second equation into the first:

[tex]b+d=50,000\\5,000+2d+d=50,000\\3d=45,000\\\\\boxed{d=15,000}[/tex]

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

With the value of [tex]d[/tex] in hand, we now solve for [tex]b[/tex] from equation(2):

[tex]b=5,000+2d\\b=5000+2(15,000)\\\boxed{b=35,000}[/tex]

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