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
Since you did not state any question, I will anticipate that you want to know how much was borrowed for each rate
amount borrowed at 2.4% --- x
amount borrowed at 4.5 % --- 10000-x
so solve for x
.024x + .045(10000-x) = 250.5
To model this situation with a linear system, we need to determine two unknowns: the amount Melissa borrowed at each interest rate.
Let's use "x" to represent the amount borrowed at 2.4%, and "y" for the amount borrowed at 4.5%.
From the problem statement, we know the following:
1. The total amount borrowed is $10,000:
x + y = 10,000
2. The total annual interest payment is $250.50:
0.024x + 0.045y = 250.50
Now we have a linear system of equations. To solve it, we can use any method, such as substitution, elimination, or matrix methods.
Let's solve it using the substitution method:
1. Start with the first equation: x + y = 10,000
Solve for x in terms of y:
x = 10,000 - y
2. Substitute this value of x into the second equation:
0.024(10,000 - y) + 0.045y = 250.50
Simplify the equation:
240 - 0.024y + 0.045y = 250.50
0.021y = 10.50
Divide both sides by 0.021:
y = 10.50 / 0.021
y = 500
3. Substitute the value of y back into the first equation to solve for x:
x + 500 = 10,000
x = 10,000 - 500
x = 9,500
Therefore, Melissa borrowed $9,500 at an interest rate of 2.4%, and $500 at an interest rate of 4.5%.