Two business partners decided to borrow $30,000 start-up money for their business. One borrowed a certain amount at a 16.5% interest rate and the other one borrowed the rest of the money at a 12.5% interest rate. How much money did each business partner borrow if the total interest amount at the end of the year was $4150?

Answer:

Step-by-step explanation:

Let's assume the first business partner borrowed x dollars and the second partner borrowed (30000 - x) dollars.

The interest earned by the first partner at a rate of 16.5% is (x * 0.165), and the interest earned by the second partner at a rate of 12.5% is ((30000 - x) * 0.125).

According to the given information, the total interest earned by both partners is $4150. So, we can write the equation:

(x * 0.165) + ((30000 - x) * 0.125) = 4150

Now, let's solve this equation to find the values of x.

0.165x + 0.125(30000 - x) = 4150

0.165x + 3750 - 0.125x = 4150

0.04x = 400

x = 400 / 0.04

x = 10000

Therefore, the first business partner borrowed $10,000 at a 16.5% interest rate, and the second partner borrowed (30000 - 10000) = $20,000 at a 12.5% interest rate.

Let's call the amount borrowed by the business partner at 16.5% "x" and the amount borrowed by the other business partner "y".

We know that the total amount borrowed is $30,000, so:

x + y = $30,000

We also know that the interest earned by the first business partner is 16.5% of x, and the interest earned by the second business partner is 12.5% of y.

So the total interest earned for the year is:

0.165x + 0.125y = $4150

We now have two equations with two unknowns, which we can solve for x and y.

First, let's isolate one of the variables in the first equation:

x = $30,000 - y

Now we can substitute this expression for x into the second equation:

0.165($30,000 - y) + 0.125y = $4150

0.165($30,000 - y) + 0.125y = $4150

$4,950 - 0.165y + 0.125y = $4150

Combine like terms:

-0.04y = $4150 - $4,950

-0.04y = -$800

Divide both sides by -0.04 to isolate y:

y = -$800 / -0.04

y = $20,000

Now that we have the value of y, we can substitute it back into the first equation to find x:

x + $20,000 = $30,000

x = $30,000 - $20,000

x = $10,000

So, the amount borrowed by the first business partner is $10,000, and the amount borrowed by the second business partner is $20,000.

100 points on this question
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