Math word problem...please help...?

Question

A realtor borrowed $90,000 to develop some property. He was able to borrow part of the money at 11.5% interest and the rest at 12%. The annual interest on the two loans amounts to $10, 525. How much was borrowed at each rate? Please show me how you arrive at the answer. Thanks

Answer 1

Two unknowns, therefore need to equations.

X + Y = $90,000
0.115 X + 0.12 Y = 10,525
In one of the equations, solve for a variable, then substitute this into the other eqn.

Y = 90,000 - X
0.115X + (0.12)(90,000-x) = 10,525
Multiply the 0.12 through the parenthesis
0.115 X +10,800 - 0.12X = 10,525
combine terms and subtract 10,800 from both sides
-0.005X = -275
multiply both side time -1
0.005 = 275
Solve for X
X = 275/ 0.005
X = $55,000

So Plug this into either eqn
55,000 + Y = $90,000
Y = $35,000

So $55,000 at 11.5% and $35,000 at 12%

;-)

Answer 2

Given the data,

Let x = amount borrowed at 11.5% and y = amount borrowed at 12%

then
(x+y)=90,000
and 11.5% times X + 12% times Y = 10,525

In this case you can either derive Y by using X = (90,000 - Y)

0.115(90,000 - Y) +0.12Y = 10,350 - 0.115Y +.12Y = 10,525
10,350+0.005Y = 10,525
0.005Y = 10,525 - 10,350
0.005Y = 175
Y = 175/0.005
Y = 35,000

If Y = 35,000 then X = (90,000 - 35,000)
X = 55,000

Conclusion $55,000 was borrowed at 11.5% and 35,000 was borrowed at 12%

(Using the same principle, you can derive X by using Y = 90,000-X and substituting in the formula accordingly.)

Answer 3

multiply by both percentages and it should total to the $10,525

$90,000 times 11.5%=

then that amount left times 12%

Answer 4

$90.000X11.5%=1035.000
1035.000X12%=???