Question 1139894: An investment of $130 comma 000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from the investments was $ 9540. The interest from the first investment was 2 times the interest from the second. Find the amounts of the three parts of the investment.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! total investment is $130,000.
investment is split into 3 parts.
first part earns 8%.
second part earns 6%
third part earns 9%.
total interest from the investments = $9540.
interest from first part = 2 * interest from second part.
let a = the amount invested in the first part.
let b = the amount invested in the second part.
let c = the amount invested in the third part.
you have two equations that need to be solved simultaneously.
they are:
a + b + c = 130,000
.08 * a + .06 * b + .09 * c = 9540
you are given that interest from the first investment is 2 times the interest from the second investment.
equation for that is .08 * a = 2 * .06 * b
divide both sides of that equaiton by .08 to get:
a = (2 * .06 * b) / .08
simplify that equation to get a = .12 * b / .08.
simplify further to get a = 1.5 * b
in the equation of a + b + c = 130,000, replace a with 1.5 * b to get a + b + c = 130,000 which becomes 1.5 * b + b + c = 130,000 which becomes 2.5 * b + c = 130,000
the first equation has now becomes 2.5 * b + c = 130,000
replace a with 1.5 * b in the second equation to get .08 * a + .06 * b + .09 * c = 9540 becomes .08 * 1.5 * b + .06 * b + .09 * c = 9540 which becomes .12 * b + .06 * b + .09 * c = 9540 which becomes .18 * b + .09 * c = 9540.
your 2 equations to solve simultaneously are now:
2.5 * b + c = 130,000
.18 * b + .09 * c = 9540
multiply both sides of the first equation by .09 and leave the second equation as is to get:
.225 * b + 09 * c = 11700
.18 * b + .09 * c = 9540
subtract the second equation from the first to get:
.045 * b = 2160
solve for b to get b = 2160 / .045 = 48,000
since a = 1.5 * b, then a = 72,000
that makes c = 10,000 because 130,000 - 48,000 - 72,000 = 10,000
a + b + c becomes 72,000 + 48,000 + 10,000 = 130,000, which is true.
.08 * a + .06 * b + .09 * c = 9540 becomes .08 * 72,000 + .06 * 48,000 + .09 * 10,000 = 9540 which becomes 5760 + 2880 + 900 = 9540 which becomes 9540 = 9540, which is true.
your solution is that the amount of the three parts of the investments are 72,000 at 8%, 48,000 at 6%, 10,000 at 9%.
|
|
|
