Question

An investment of $82,000 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 $6300. The interest from the first investment was 4 times the interest from the second. Find the amounts of the three parts of the investment. What is the amount of the first part of the investment?
1. What is the amount of the first part of the investment?
2. What is the amount of the second part of the investment?
3. What is the amount of the third part of the investment

Answer 1

Answer:

a 54,000 dolllars

b 18,000 dollars

c 10,000 dollars

Explanation:

From the given we can conclude:

all investment equal 82,000 thus:

82,000= a + b + c

then:

interest of a equal 4 times interest of b:

a x 0.08 = 4 x b x 0.06

a =  (0.24/0.08)b = 3b

and that total interest:

a x 0.08 + b x 0.06 + c x 0.09 = 6,300

4 x b x 0.06 + b x 0.06 + c x 0.09 = 6,300

5bx0.06 + 0.09c = 6,300

c = (6,300 - 0.3b)/0.09

we now replace a and c as expressions of b:

82,000 = 3b + b + c = 4b + c

82,000 = 4b + (6,300 - 0.3b)/0.09

82,000 = 4b + 70,000 - 3,33b

12,000 = (2/3)b

b = 18,000

now we solve for a and c:

a = 3b = 3 x 18,000 = 54,000

interest of b:

18,000 x 0.06 = 1,080

interest of a:

54,000 x 0.08 = 4.320‬

4,320/1,080 = 4 we pass the interest relathionship requirement

82,000 - 54,000 - 18,000 = c

c= 10,000

10,000 x 0.09 = 900

1,080 + 4,320 + 900 = 6,300 we also fullfil the total interst requirement