college algebra word problem

Question

Aldo borrowed a total of $4000

 from two student loans. One loan charged 4%

 simple interest and the other charged 3.5%

 simple interest, both payable after graduation. If the interest he owed after 3

 years was $450

, determine the amount of principal for each loan.

Answer 1

The ask of the problem is to find the principal amount for each loan so let's assign these as P1 and P2 respectively.

Total principal borrowed is 4000$ that means P1 + P2 = 4000

P1 = 4000 - P2 ............................. (1)

Each loan has it's own interest rate. Let's assume P1 charges 4% and P2 charges 3.5% simple interest rate.

Formula to calculate simple interest is as follows:

SI = P*R*T / 100, where P is principal amount, R is interest rate, and T is time period.

Let's say he has I1 simple interest on P1 and I2 simple interest on P2. Applying the above formula, we get

I1 = (P1 * 4 * 3)/100

= 12P1/100

I2 = (P2 * 3.5 * 3)/100

= 10.5P2/100

He owed 450$ in interest after 3 years, that means

I1 + I2 = 450

(12P1 + 10.5P2)/100 = 450 ................................................. (2)

Substitute equation (1) in (2) and find values for P1 and P2 which are 2000$ each.

Answer 2

a + b = 4000

3(0.04a + 0.035b) = 450

a = 4000 - b

0.04a + 0.035b = 150

0.04(4000 - b) + 0.035b = 150

160 - 0.04b + 0.035b = 150

-0.005b = -10

b = $2000

a = 4000 - 2000

a = $2000

$2000 in each