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
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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) (Show Source): You can put this solution on YOUR website!
Solution;
suppose $ was lent at % per annum:
thus,
Therefore
$
Answer by Theo(13342) (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.
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