Question

In the following exercises, translate to a system of equations and solve the system.

Daniela invested a total of \(50,000, some in a certificate of deposit (CD) and the remainder in bonds. The amount invested in bonds was \)5000 more than twice the amount she put into the CD. How much did she invest in each account?

Short answer

The amount invested into CD $15,000 and the amount invested into bonds is $35,000

Step-by-step solution

Step 1. Given Information

The given data is that 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 $5000 more than twice the amount she put into the CD.

Step 2. Explanation

Let the amount invested in CD be x and the amount invested in bonds be y.

Total amount invested is $50,000 that is $x+y=50000--\left(1\right)$

The amount invested in bonds was $5000 more than twice the amount she put into the CD that is$y=2x+5000--\left(2\right)$

Step 3. Calculation

Substitute the equation (2) in equation (1) and simplify to get one of the number.

$$\begin{gathered} x+2x+5000=50000 \\ 3x=45000 \\ x=15000 \end{gathered}$$

Substitute the value of x in the equation (2) to get the value of y.

$$\begin{gathered} y=2\left(15000\right)+5000 \\ y=35000 \end{gathered}$$