# 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**