Question

An investment of $27,000 was made by a business club.The investment was split into three parts and lasted for 1 year.The first part earned 8% interest,the second 6% and the third 9%.total interest from the investment was $2130.the interest from the first investment was three times the interest from the second find the amounts of the three parts of investments

Answer 1

Find out the amounts of the three parts of investments .

To proof

let us assume that first part of investment be = u

let us assume that second part of investment be = v

let us assume that third part of investment be = w

As given

An investment of $27,000 was made by a business club.The investment was split into three parts and lasted for 1 year.

than the equation is written in the form

u + v + w = 27000

.The first part earned 8% interest,the second 6% and the third 9%.total interest from the investment was $2130.

8% is written in the decimal form

`=(8)/(100)`

= 0.08

6% is written in the decimal form

`=(6)/(100)`

= 0.06

9% is written in the decimal form

`=(9)/(100)`

= 0.09

than the equation in the form

0.08u +0.06v +0.09w = 2130

equation written in the simple form

8u +6v +9w =213000

As given

the first investment was three times the interest from the second

u = 3v

Than the three equation in the form

u + v + w = 27000 , 8u +6v +9w =213000 , u = 3v

put this u = 3v in the equation u + v + w = 27000 , 8u +6v +9w =213000

than the equation

30v +9w + 213000

4v +w = 27000

multiply the 4v +w = 27000 by 9 and subtracted with 30v +9w + 213000

36v-30v +9w-9w =243000- 213000

6v = 30000

`v =(30000)/(6)`

v =$5000

put this in the equation

u =3v

u = 3× 5000

u= $15000

put the value u , v in the equation u + v + w = 27000

5000 + 15000 +w = 27000

w = $7000

than the three part be $5000, $15000,$7000

Hence proved