Invested Amount

Algebra

Invested Amount

A, B, C, and D invest s dollars in a transaction. B invests m times as much as A; C equals as much as A and B together; D equals as much as C and B together. Determine amt. each invests.

A = Bm

C = A + B

D = C + B

Not sure how to proceed.
Guest

Re: Invested Amount

Good afternoon!!

$$B=mA\\ C=A+B=A+mA=(1+m)A\\ D=C+B=(1+m)A+mA=(1+2m)A\\ A+B+C+D=s\\ A+mA+(1+m)A+(1+2m)A=s\\ A(1+m+1+m+1+2m)=s\\ \boxed{A(3+4m)=s}\Rightarrow \boxed{ \begin{cases} A=\dfrac{s}{3+4m}\\\\ B=\dfrac{ms}{3+4m}\\\\ C=\dfrac{(1+m)s}{3+4m}\\\\ D=\dfrac{(1+2m)s}{3+4m} \end{cases}}$$

Hope to Have Helped! (3H)

Baltuilhe

Posts: 97
Joined: Fri Dec 14, 2018 3:55 pm
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Re: Invested Amount

Good Afternoon!

Ok, Thanks again.
Guest