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

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

To solve this problem, we can break it down into three equations using the information given.

Let's assume the first investment amount is x.
So, the second investment amount is (x/3) since the interest from the first investment was three times the interest from the second.
The third investment amount can be expressed as (27,000 - x - x/3).

Now, let's calculate the interest earned from each investment:

1. Interest from the first investment: 8% of x = 0.08x
2. Interest from the second investment: 6% of (x/3) = 0.06(x/3)
3. Interest from the third investment: 9% of (27,000 - x - x/3) = 0.09(27,000 - 4x/3)

According to the problem, the total interest from the investment is $2,130, so we can write the equation:

0.08x + 0.06(x/3) + 0.09(27,000 - 4x/3) = 2,130

To solve this equation, we can simplify and rearrange:

0.08x + 0.02x + 2,430 - 0.04x = 2,130
0.06x = 2,130 - 2,430
0.06x = -300
x = -300 / 0.06
x ≈ 5,000

Now that we have the value of x, we can calculate the other investment amounts:

First investment: x = $5,000
Second investment: x/3 = $5,000/3 ≈ $1,666.67
Third investment: 27,000 - x - x/3 = 27,000 - 5,000 - (5,000/3) ≈ $20,333.33

Therefore, the amounts of the three parts of the investments are approximately: $5,000, $1,666.67, and $20,333.33.

Answer 2

first investment ---- x

2nd investment --- y
3rd investment --- z

.08x + .06y + .09z = 2130 ---> 8x+6y+9z = 213,000 **
x+y+z = 27,000 ***

given: .08x = 3(.06)y
8x = 18y
y = 4x/9
sub into ** 8x+6x+9z = 213,000
8x + 8x/3 + 9z = 213,000
32x + 27z = 639,000 ##

sub into *** x+y+z = 27,000
x + 4x/9 + z = 27000
9x + 4x + 9z = 243,000
13x + 9z = 243,000 ###

3 times ### ---> 39x + 27z = 729,000
subtract ##
7x = 90,000
x = 90,000/7

find y, then backsub into ***