Question

A total of $91,000 is to be​ invested, some in bonds and some in certificates of deposit​ (CDs). If the amount invested in bonds is to exceed that in CDs by $8 ,000 comma how much will be invested in each type of​ investment?

Answer 1

Answer:

CD:        41,500

Bonds:  49,500

Explanation:

Base on the information we are given, we can create an equation system:

The total investment in bonds and certificates of deposit totals 91,000

and the amount investment on bonds are 8,000 higher than Certificates of deposit

$\left \{ {{CD + Bonds = 91,000} \atop {Bonds = CD + 8,000}} \right.$

We replace the bonds of the second equation on the first equation:

CD + (CD + 8,000) = 91,000

And solve for certificates of deposits

2CD = 91,000 - 8,000

CD = 83,000/2 = 41,500

Now, we replace the CD on the second equation

Bonds = CD + 8,000

Bonds = 41,500 + 8,000 = 49,500

Answer 2

The amount of invested amount in each kind of investment should be $415,00 and $49,500 respectively.  

Calculation of amount invested:

Here we assume the certificate of deposit be x

So, the bond should be $91000 - x

Now

the equation should be

($91,000 - x) - x = $8,000

$91,000 - 2x = $8,000

$83,000 = 2x

x = $41,500

So, the bond should be

= $91,000 - $41,500

= $49,500

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