SOLUTION: please help me solving it.i tried it again and again but still not getting it. some amount out of $7000 was lent at 6% p.a. and the remaining was lent at 4%p.a. if the total simp

Algebra ->  Finance -> SOLUTION: please help me solving it.i tried it again and again but still not getting it. some amount out of $7000 was lent at 6% p.a. and the remaining was lent at 4%p.a. if the total simp      Log On


   

Question 935621: please help me solving it.i tried it again and again but still not getting it. some amount out of $7000 was lent at 6% p.a. and the remaining was lent at 4%p.a.
if the total simple interest in 5 years was $1600, find the amount lent 6% p.a
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Solution;
suppose $ x was lent at 6% per annum:
thus,

%28x%2A6%2A5%29%2F100+%2B+%28%287000-x%29%2A4%2A5%29%2F100=1600
3x%2F10+%2B+%2814000-2x%29%2F10=1600
3x%2F10+%2B+%28cross%2814000%297000-cross%282%29x%29%2Fcross%2810%295=1600
3x%2F10%2B%287000-x%29%2F5=1600
3x%2B%287000-x%292=1600%2A10
3x%2B14000-2x=16000
Therefore
x=16000-14000
$ x=2000

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x equal the amount invested at 6%.
let y equal the amount invested at 4%.

total amount invested is 7000, so x + y = 7000

simple interest formula is:

i = n * r * p

i = total interest
n = number of years
r = annual rate of interest
p = principal

x is the principal that is invested at 6%.
y is the principal that is invested at 4%.

total interest is 1600, so 5 * .06 * x + 5 * .04 * y = 1600

you have 2 equations that need to be solved simultaneously.

they are:

x + y = 7000
5 * .06 * x + 5 * .04 * y = 1600

simplify the second equation to get:

5 * .06 * x + 5 * .04 * y = 1600 becomes:
.3 * x + .2 * y = 1600

your 2 equations now are:

x + y = 7000
.3 * x + .2 * y = 1600

solve for y in the first equation to get y = 7000 - x.

substitute 7000 - x for y in the second equation to get:

.3 * x + .2 * (7000 - x) = 1600

solve for x in this equation:

start with:
.3 * x + .2 * (7000 - x) = 1600
distribute the multiplication to get:
.3 * x + .2 * 7000 - .2 * x = 1600
simplify to get:
.3 * x + 1400 - .2 * x = 1600
combine like terms to get:
.1 * x + 1400 = 1600
subtract 1400 from both sides of the equation to get:
.1 * x = 200
divide both sides of the equation by .1 to get:
x = 2000

since x + y = 7000, and x = 2000, then y must be equal to 5000.

x + y = 7000 becomes 2000 + 5000 = 7000 which becomes 7000 = 7000 which is good.

5 * .06 * x + 5 * .04 * y = 1600 becomes .3 * 2000 + .2 * 5000 = 1600 which becomes 600 + 1000 = 1600 which becomes 1600 = 1600 which is also good.

the solution looks good and your answer is that the amount lent at 6% per year is equal to 2000.