An investment of $93,000 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 earned 6% and the third 9%. total interest from the investments was $7110. The interest from the first investment was 3 times the interest from the second. Find the amounts of the three parts of th investment??
second part --- x
first part ---- 3x
third part --- (93000 - x - 3x) = 93000 - 4x
.08(3x) + .06x + .09(93000-4x) = 7110
.24x + .06x + 8370 - .36x = 7110
-.06x = -1260
x = -1260/-.06 = 21000
second investment = x = $21000
first investment = 3x = $63000
third investment = 93000-4x = $9000
check:
63000(.08) + 21000(.06) + 9000(.09) = 7110
for twenty years
Well, it seems like this business club certainly knows how to divide their money and have some fun with it!
Let's break down this hilarious investment puzzle. We'll call the amount of money invested in the first part "x." Since the interest from the first investment was three times that of the second investment, the interest from the second part would be "x/3."
Now, let's calculate the interests for each investment part. The interest from the first part (8% interest) would be 0.08x, the interest from the second part (6% interest) would be 0.06(x/3), and the interest from the third part (9% interest) would be 0.09(93000 - x - x/3).
To find the total interest, we add up the interests from each part:
0.08x + 0.06(x/3) + 0.09(93000 - x - x/3) = 7110.
Now, let the laughter begin as we solve this equation:
0.08x + 0.02x + 0.09(93000 - 4x/3) = 7110
Simplifying further, we have:
0.08x + 0.02x + 8370 - 0.36x = 7110
Let's continue the clownery by combining like terms and isolating the "x" term:
0.08x + 0.02x - 0.36x = 7110 - 8370
-0.26x = -1260
Finally, let's take the x out of its misery by dividing both sides by -0.26:
x = 1260 / 0.26
Voila! We've found that x, the investment in the first part, is approximately $4,846.15. That means the second part of the investment would be $4,846.15 / 3, which is approximately $1,615.38. And to calculate the third part, we subtract the sum of the first two parts from the total investment of $93,000, so it would be approximately $93,000 - $4,846.15 - $1,615.38, which is approximately $86,538.47.
So, to recap the circus act, the amounts invested in the three parts are approximately $4,846.15, $1,615.38, and $86,538.47, respectively.
Remember, investing can be a serious business, but adding a dash of humor always makes the numbers dance better!
To solve this problem, let's break it down step by step.
Let's assume the first part of the investment is x dollars. Since the interest earned from the first investment is 3 times the interest earned from the second, we know that the interest earned from the second investment is (1/3) * interest earned from the first investment.
Now, we can calculate the interest earned from each part of the investment.
The interest earned from the first part of the investment (x dollars) at 8% interest rate can be calculated as (8/100) * x = 0.08x.
The interest earned from the second part of the investment at 6% interest rate can be calculated as (6/100) * (1/3) * x = 0.02x.
The interest earned from the third part of the investment (93,000 - x - (1/3) * x) at 9% interest rate can be calculated as (9/100) * (93,000 - x - (1/3) * x) = 0.09(93,000 - x - (1/3) * x).
Now, we can set up an equation to solve for x:
0.08x + 0.02x + 0.09(93,000 - x - (1/3) * x) = 7,110.
Simplifying the equation gives us:
0.08x + 0.02x + 0.09(93,000 - x - (1/3) * x) = 7,110
0.08x + 0.02x + 8,370 - 0.09x - 0.03x = 7,110
0.08x + 0.02x + 8,370 - 0.09x - 0.03x = 7,110
0.13x + 8,370 - 0.12x = 7,110
0.01x = 7,110 - 8,370
0.01x = -1,260
x = -1,260 / 0.01
x = -126,000
From the calculation, we find that the value of x is negative, which doesn't make sense in the context of the problem. This means there is no valid solution for the problem as stated.
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