SOLUTION: To buy both a new car and a new house, Tina sought two loans totalling $191,610. The simple interest rate on the first loan was 6.3%, while the simple interest rate on the second l

Question 548945: To buy both a new car and a new house, Tina sought two loans totalling $191,610. The simple interest rate on the first loan was 6.3%, while the simple interest rate on the second loan was 8.8%. At the end of the first year, Tina paid a combined interest payment of $16,681.66. What were the amounts of the two loans?
How do I set up and answer
Found 2 solutions by mananth, josmiceli:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Fund A 6.30% per annum ---x
Fund B 8.80% per annum ---y

x+y=191610 ------------------------1
6.30%x+ 8.80%y= =$16,681.66
Multiply by100
6.3x+8.8y=$1,668,166.00 --------2

Multiply (1) by -6.3
we get

-6.3x-6.3y=-1207143.00

Add this to (2)

0x+2.5y=$461,023.00

divide by2.5

y = $184,409.20 investment at 8.80%
Balance $7,200.80 investment at 6.30%
CHECK
$7,200.80 --------- 6.30% ------- $453.65
$184,409.20 ------- 8.80% ------- $16,228.01
Total -------------- $16,681.66
m.ananth@hotmail.ca

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The formula for simple interest is

= amount after years
= original amount
= annual % interest rate
----------------------------------
Let the equation for the 1st loan be

Let the equation for the 2nd loan be

given:

and
Adding the 2 equations with

The combined interest payment is
(1)
But also
(2)
Multiply both sides of (2) by
and subtract (2) from (1)
(1)
(2)

and,
(2)
(2)
(2)
The amounts of the loans were:
$7,200.80 @ 6.3%
$184,409.20 @ 8.8%
check:
( = 1 )

The combined interest payment should be

This is correct

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