Question

Homework: Section 1.2 Homework

Jamal borrowed $3,000 to buy a used car. He borrowed some of the money from a bank that charged 5.2% simple interest and the rest from a friend who charged 10% simple interest. If the total interest for a one-year loan was
$228.00, how much did Jamal borrow at each rate?
C
Jamal borrowed at 5.2% simple interest and sat 10% simple interest
(Simplify your answers )

Answer 1

Jamal borrowed $1500 at 5.2% simple interest and $1500 at 10% simple interest.

Step-by-step explanation:

Let's call x the amount borrowed at 5.2% and y the amount borrowed at 10% simple interest.

He borrowed $3000 in total, so

x + y = 3000

On the other hand, the total interest was $228, so

0.052x + 0.1y = 228

Because 0.052x is the interest for the bank and 0.1y is the interest for his friend.

Now, we can solve the first equation for y

x + y - x = 3000 - x

y = 3000 - x

Then, replace this on the second equation

0.052x + 0.1(3000 - x) = 228

Solve for x

0.052x + 0.1(3000) - 0.1x = 228

-0.048x + 300 = 228

-0.048x + 300 - 300 = 228 - 300

-0.048x = -72

-0.048x/(-0.048) = -72/(-0.048)

x = 1500

With the value of x, we can find the value of y, so

y = 3000 - x

y = 3000 - 1500

y = 1500

Therefore, Jamal borrowed $1500 at 5.2% simple interest and $1500 at 10% simple interest.