Model this situation w/ a linear system:
Melissa borrowed $10, 000 for her university tuition. She borrowed part of the money at an annual interest rate of 2.4 % and the rest of the money at an annual rate of 4.5 %. Her total annual interest payment is $ 250.50
a.) a + b = 10 000 & 0.024a + 0.045b = $250.50
b.) 2a + 2b = 10 000 & 0.024a + 0.045 b = $250.50
c.) 0.024a + b = 10 000 & a + 0.045b = $250.50
d.) a + b = $250.50 & 0.024a + 0.045b = 10 000
which letter is correct?
What do you think, and why?
no idea . please help!
The correct answer is option a.) a + b = 10,000 & 0.024a + 0.045b = $250.50.
To model this situation with a linear system, we need to set up two equations representing the given information.
Let's denote the amount borrowed at 2.4% interest rate as 'a' and the amount borrowed at 4.5% interest rate as 'b'.
From the problem, we know that Melissa borrowed a total of $10,000. This can be represented by the equation a + b = 10,000.
We also know that her total annual interest payment is $250.50. The interest payment on the amount borrowed at 2.4% interest rate is 0.024a, and the interest payment on the amount borrowed at 4.5% interest rate is 0.045b. So, we can represent this information with the equation 0.024a + 0.045b = $250.50.
Therefore, the correct linear system representing this situation is:
a + b = 10,000
0.024a + 0.045b = $250.50