An investor has $1100 income from bonds bearing 4% and 5%. If the amounts at 4% and 5% were interchanged, she would earn $50 more per year. Find the total sum invested.

So, let's set this up:

0.04x+0.05y=1100
0.05x+0.04y=1150

Let's multiply each equation by 100:
4x+5y=110000
5x+4y=115000

Now let's add those together:

9x+9y=225000

And we need to find x+y, so we just divide by 9 and get 25,000

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Yogeshkumari Yogeshkumari · Answer 2 · 2022-05-31T16:08:37+02:00

Total sum invested is equals to $25,000.

What is the system of equations?

" A system of equation is a finite set of equations for which we find the common solution."

According to the question,

Situation1: Investor has $1100 income from bonds bearing 4% and 5%.

'x' represents investment amount at 4%.

'y' represents investment amount at 5%.

Equation :

(4/100)x + ( 5/100)y =1100

⇒ 4x + 5y = 110,000 ____(1)

Situation 2: Amount at 4% and 5% were interchanged, investor earned $50 more per year.

Equation:

(5/100)x + ( 4/100)y =1150

⇒ 5x + 4y = 115,000 ____(2)

Add equation (1) and (2) we get,

9x + 9y = 225,000

⇒x + y = (225,000 / 9)

⇒ x+ y = $25,000

Hence, total sum invested is x+ y =$25,000.

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