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Advanced Math/Amount Invested


QUESTION: A, B, C, and D invest $s.  B invests m times as much as A, C as much as A and B combined, and D as much as C and B combined.  Determine amount each invests.

Answers given with problem:

A: s / 3 + 4m

B: ms / 3 + 4m

C: s(1 + m) / 3 + 4m

D: s(1 + 2m) / 3 + 4m

How do I solve?  Thanks.

ANSWER: "A, B, C, and D invest $s."
A+B+C+D = s

"B invests m times as much as A"
B = mA

"C invests as much as A and B combined"
C = A+B = A+(mA) = A(m+1)

"D invests as much as C and B combined"
D = C+B = A(m+1) + mA = A(2m+1)

A+B+C+D = A + mA + A(m+1) + A(2m+1) = A(4m+3)
A(4m+3) = s
A = s/(4m+3)
B = mA = ms/(4m+3)
C = (m+1)A = (m+1)s/(4m+3)
D = (2m+1)A = (2m+1)s/(4m+3)

Note that the denominators need parentheses, too.

---------- FOLLOW-UP ----------

QUESTION: A couple of questions:

1. How did you obtain C = A(m + 1)?

2. Why is each divided by (4m+3)?

Thanks again.

B = mA
C = A+B

By substitution, C = A + mA.
By the distributive rule, A + mA = A(1+m).
D = C+B
By substitution, D = A(m+1) + mA.
By the distributive rule, D = A(2m+1).

It is given that A+B+C+D = s.
By subsitution, A(4m+3) = s.
A = s/(4m+3)

Since B, C, and D are expressed in terms of A, they all have denominators of 4m+3.

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