if A/B= 1/4, B/C= 3/2 and C/D= 2/5, then what is the value of A + B + C+ D
You asked:
Given the following equations: \[\begin{aligned}\frac{A}{B} &= \frac{1}{4}\\ \frac{B}{C} &= \frac{3}{2}\\ \frac{C}{D} &= \frac{2}{5}\end{aligned}\] Evaluate \(A + B + C + D\).
MathBot Answer:
The system of equations has infinitely many solutions.
$$\begin{aligned}A &= \frac{3 D}{20}\\B &= \frac{3 D}{5}\\C &= \frac{2 D}{5}\end{aligned}$$
By substituting these values into the expression, we find that: $$\begin{aligned}A + B + C + D &= \frac{43 D}{20}\end{aligned}$$