SOLUTION: To buy both a new car and a new house, Tina sought two loans totalling $321,929. The simple interest rate on the first loan was 1.0%, while the simple interest rate on the second l

Algebra ->  Expressions-with-variables -> SOLUTION: To buy both a new car and a new house, Tina sought two loans totalling $321,929. The simple interest rate on the first loan was 1.0%, while the simple interest rate on the second l      Log On


   

Question 562781: To buy both a new car and a new house, Tina sought two loans totalling $321,929. The simple interest rate on the first loan was 1.0%, 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 $25,677.83. What were the amounts of the two loans?
I think i know the answer but could someone please help me work out this problem?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the price of the house and y be the price of the car
x%2By=321929
The interest on the house is 0.01x.
The interest on the car is 0.088y
The total interest for the first year is
0.01x%2B0.088y=25677.83
Multiplying times 100 to get rid of some decimals
x%2B8.8y=2567783
The equations
x%2B8.8y=2567783 and
x%2By=321929 form a system of linear equations.
It could be solved several different ways.
For example, subtracting the second equation from the first one we get
x%2B8.8y-x-y=2567783-321929 which simplifies to
7.8y=2245854 and dividing both sides by 7.8, we get
y=2245854%2F7.8=287930
Substituting that into x%2By=321929 we get
x%2B287930=321929 --> x=321929-287930=33999
Tina bought a house for $33,999 and a car for $287,930.
Very strange.