Question

A soil supplement that weighs 19 lb contains iron, potassium, and mulch. The supplement contains sixteen times as much mulch as iron and twice as much potassium as iron. Find the amount of mulch in the soil supplement.

Answer 1

So.. let's say iron (f) plus potassium(k) plus mulch(m) all those quantities added together, whatever they are, add up to 19lbs
thus

f + k + m = 19

there is 16 times more mulch than iron, thus m = 16f
and twice as much as potassium, thus m = 2k

so   $\bf f+k+m=19\qquad \begin{cases} f=iron\\ k=potassium\\ m=mulch\\ --------------\\ m=16f\to \frac{m}{16}=\boxed{f} \\\\ m=2k\to \frac{m}{2}=\boxed{k} \end{cases} \\\\\\ \cfrac{m}{16}+\cfrac{m}{2}+m=19$

solve for "m", to see how much mulch there is

how much iron?  well, m/16 = f

how much potassium?  well, m/2 = k