Mixing Problems Calculus

mixing problems calculus
Investment Math Word Problem Help…?

Can you guy’s help me do this problem, there are no examples in my textbook, Finite Math…
I’ve always hated word problems, I can do some calculus word problems like mixing and such, yet investment eludes me for some reason… I find that I learn best by example… I just don’t know how to set this up, I’ve tried multiple ways, even the echelon method.

An investment of $44,000 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 investment was $3,600. The interest from the first investment was 4 times the interest from the second. Find the amounts of the three parts Invested.
Thanks, that answered all my questions and helped me out an enormous amount.

First investment:
Principal = p
Rate = 0.08
Interest = 0.08p

Second investment:
Principal = 0.02p/0.06 = 1/3 p
Rate = 0.06
Interest = (1/4)(0.08p) = 0.02p

Third investment:
Principal = 44000 – p – 1/3 p = 44000 – 4/3 p
Rate = 0.09
Interest = 0.09(44000 – 4/3 p) = 3960 – 0.12p

Add the interest amounts together from all three investments. The total is $3600:

0.08p + 0.02p + 3960 – 0.12p = 3600

Solve for p:

—> -0.02p = -360

—> p = 18000

First investment:
Principal = p = $18,000

Second investment:
Principal = 0.02p/0.06 = 1/3 p = 1/3(18000) = $6000

Third investment:
Principal = 44000 – p – 1/3 p = 44000 – 4/3 p = 44000 – 4/3(18000) = 44000 – 24000 = $20,000

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Mixing Problems and Separable Differential Equations

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