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

To find the amount of mulch in the soil supplement, define the weight of iron as x pounds. Using the ratios given, set up the equation: x + 16x + 2x = 19, which simplifies to 19x = 19, meaning x = 1 pound of iron. Multiply by 16 to get 16 pounds of mulch.

Step-by-step explanation:

The student is asking how to find the amount of mulch in a soil supplement where the weight of the supplement is 19 lb and it contains iron, potassium, and mulch in a specific ratio. We are told that the supplement has sixteen times as much mulch as iron and twice as much potassium as iron. Let's define the weight of iron as x pounds. Therefore, the mulch is 16x pounds, and the potassium is 2x pounds.

Now, let's set up the equation based on the total weight of the supplement:

x + 16x + 2x = 19

Combining like terms, we get:19x = 19

Dividing both sides by 19, we find:

x = 1

Thus, the weight of iron is 1 lb. Now, to find the amount of mulch, we multiply this by 16:

16 x 1 = 16 lb

So, there are 16 pounds of mulch in the soil supplement.

Answer 2

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 (m)/(16)=\boxed{f} \\\\ m=2k\to (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